This is long, but I hope it gives you an idea as to where to start. I am giving as much info as possible to help others who have children UNDER 3, as well as OVER 3.
My son does the same thing. We noticed at about 2 1/2 simply because my stepson (who is now 24) is 87% deaf. So when we started this, we were going in to this with my husband thinking our youngest was also deaf, but I KNEW he wasn't. I could softly say things like ice cream in one room and he'd come running from the other room :) Thankfully my husband insisted on getting him checked. It has made all of the difference in the world.
I just thought he was "average" compared with our daughter who was speaking complete phrases such as "How disgusting. Somebody has really bad gas!" at the age 18 months and EVERYBODY could understand her. No exaggeration - she really said that at a party when an uncle let out an SBD (silent but deadly). It was hilarious! She had a vocabulary that most kids don't develop until 1st or second grade because she hears "big" words in everyday conversation and we will give a definition if the kids ask. She is 8 1/2 but can read on a 12 year old level or higher.
Some people will say "she'll grow out of it", but what if she doesn't? She then won't get help until Kindergarten which will be even more frustrating for her. Because he started speaking late, my son does have a bit of "baby sound" to his speech. He has the vocabulary of a 1st grader, but his voice sounds like a 3 year old compared to other 5 year olds because of his pronunciation. My son is just-turned-five and is just now, over the last few months, getting a grasp on the sounds of the Alphabet because he didn't know how to make his mouth work. Since he couldn't say them, he didn't want to learn them. He LOVES the DVD by LeapFrog called "The Letter Factory". It has helped so much in pronouncing the letters he sees. It teaches more of the SOUNDS of the letters than the NAMES, which for him is more important to me.
First, we have never spoken "baby" to him or our daughter, but he had "baby" words for most of everything. He would say the baby word, I would repeat the real word (if I figured it out), then he would say "yes, that", repeat it as correctly as he could and the next time he would say it his way again. If not, then he grew so frustrated that he would literally hit himself on the head or bang his head on the wall or cabinet or start throwing things - not a typical temper tantrum, but almost grown man sized anger. He was not playing any "games" about this, he was truly having a problem with making the words come out right. That has gone away since he can make himself understood now. Now it's just "go to the corner, 5 year old" tanrums once in a great while.
I could only truly understand about 30% of what he said and the rest I translated out of what I knew he was TRYING to say, my husband could only understand about 15% and I had to translate everything else for him, strangers could not understand him but maybe 10% of the time. My little one would repeat what he was saying over and over and over again until he just flew into a rage totally out of proportion for a 2-3 year old. He has gotten really good at charades because he would act out what he tried to say if he couldn't make us understand. Here's what we did to get help.
We took him to his pediatrician and got a referral to a Pediatriac Ear, Nose and Throat doctor. Our Health Insurance covered the tests, we just paid our usual Specialist co-pays. They set him up for a sedated hearing test. This is done in a hospital so that he has a bed to lie in and all that. They give him a med to make him sleepy and place an earbud that is hooked up to a computer in one ear and do a series of tests (they cover things like sounds to pressure in the ear), then do the other side. Be prepared, my son fought the meds, so they had to give about 3 doses before he would even just lie quietly for a while. They err on the side of caution and don't give "big" doses to begin with, so it's a little at a time. My son had a slight cold that morning, so his right ear showed a little bit of pressure that they were concerned about, but they didn't push about it since I knew he had a stuffy nose that day.
Next they set him up for the hearing test in the ENT's office where he sits in a little room and they activate sounds of different levels around him to see if he looks at the sounds. They let me sit with him in my lap, so long as I just sat there and didn't give ANY hints to him about where the sounds were coming from. This is more helpful at this age because some kids this age don't always understand the "raise your left hand when you hear something in your left ear and your right hand for your right ear" instructions.
After all of the tests, my son was diagnosed with hearing that is as perfect as possible. He is extremely intelligent like your little one. They recommended that I call Early Childhood Intervention (ECI) since he was under the age of 3. He only qualifies until age 3. They receive grants which fund them. My husband was making about $35,000 with a family of 4 at the time and we were covered by the Family Cost Share. They recently REALLY raised how much you can make and still receive free services. They can also help you with what you need to know about contacting your school, since she's three. Through your school district, it is at NO EXTRA charge to you. It is paid for by school taxes. They got me in contact with Brighton Learning and they verified that my son had a speech delay, not a learning diability. After this, I started making lists of which sounds he said correctly, which sounds he substitued for others, how he dropped the beginning, middle AND endings of words and just said the vowel sounds (ih-e instead if Sissy - he still calls his sister E-E and E-on because he can't pronounce the v in Yvie or Yvonne), naming a stuffed animal "gah-gah" instead "dog-dog" because he would switch the beginning and ending sounds, drop the 'd' but keep the middle sounds in place, which words he couldn't wrap his little mind around, which words he added to his "correctly said" list, etc.
http://www.dars.state.tx.us/ecis/FCSFeeScale.pdf This is the page for the fee scale.
http://www.dars.state.tx.us/ecis/index.shtml This is the website about ECI.
Once he turned 3, we had to contact our elementary school. Thankfully it's the one he will attend for Kinder. First we had to fill out the enrollment forms as if he were starting Kinder: shot records, SSN, proof of residency, vision and hearing exams (plenty of those), etc. We took in all of the hearing test results.
First they set up a test for my son with the Speech Pathologist. It asks A LOT of questions. It tests where the child is developmentally, but more importantly it shows the Speech Pathologist how he pronounces words, which sounds he knows and doesn't know, how he mispronounces sounds and words, which sounds he mixes up, etc. The test can take a while and we actually had to let him stop for the morning because it ran into his nap time and he stopped responding to questions that I knew he knew the anwers to, so we set up an appointment to come back and finish the test. I never helped him answer, but sometimes I would help ask a question the way he had heard it before with out telling him what to say. It was good that I didn't "give" him answers because that can give him a better score than he deserved and he wouldn't have qualified for help.
They then set up a meeting with us called an ARD: Admissions, Reviews, & Dismissals. This is a meeting with the Speech Pathologist and a school counselor. It helps in placing children with Special Needs in the correct classes, whether it is for speech or for Down's Syndrome. They do not lump each Need with all of the others, they group them according to the help needed. They went over the results of his test. On his knowledge for his age he got an 86% which just means that he he's right on target for what he is supposed to know (no parent can teach their child 100% of everything). However, on what he could SAY OUT LOUD he received a whopping score of 9%! He was correctly saying 9% of what a 3 year old should be able to say. What my husband and I had noticed and what I had listed from the beginning was pretty much on the nose.
The problem my son has been diagnosed with is that his brain KNOWS the word. He thinks the word, tries to say the word and it gets all mixed up when his mouth tries to form the word. What his teacher is helping him do is think how his mouth needs to move to make each sound in combination with other sounds to make the word.
My son began 30 minute classes twice a week. He did not qualify for Pre-K based on my husband's income or any of the other requirements for Pre-K. I'm a SAHM, so scheduling is not an issue for me. The only other way he could have qualified is if I had pushed for him to be labeled "Special Needs" in other areas. They suggested that I not do that since he doesn't have any mental or physical challenges because this would have stayed on his school record and is difficult to remove later. "Why do you want the Special Needs taken off his record? If he is not Special Needs why did you have him labeled that way? etc." Hard to prove he's not special needs if I had lied to get him in.
He has been going class for the last 2 years. They work on specific sounds at a time. They started with final k, until he could say that without being reminded most of the time, the to another sound, always working with ONE sound at a time until he was usually saying the sound on his own or correcting himself on his own with that sound. He loves class and he loves his teacher, Miss Christa. He has gone from being understood by only me, to being understandable to strangers about 80% of the time, unless he gets excited and starts talking too fast to control his speech... Just mention trains and I have to either start translating or try to make him slow down and think about forming his words. He speaks slower now and with more forethought. If he can't remember how to say a word, he'll stop and ask "Mommy, what's that word I'm thinking 'bout?" or "How do say it again?" I ask him what the word means, he'll define the word and I'll ask "Do you mean /this/?" "Yeah! That's word! /this/!" My son has gotten to the point where he will say a word wrong, stop, and repeat the word correctly or ask for help. I watch him as he speaks so that I can tell if he's having trouble with a particular word. When he says a word incorrectly, we just ask him to repeat it once or twice, then go on. We don't have "class time" at home. We just work on it as it comes up. His teacher says that is really a good way of not making him self-concious but still making him think about forming his sounds. Sometimes he will say it's time to "work on his words" and will work on the words his teacher sends home or reinforce words/sounds he has already gotten pretty good at.
He gets reviewed every year on how he's doing and when they AND we feel he no longer needs help, then he will no longer go to speech class. For now though, he will start Kinder this fall and will only be taken out of his regular classroom twice a week for half an hour, and he will have speech class with other students then. Since he wasn't in a "class" this year he had solo sessions.
My husband was away for a week recently and we noticed that my son spoke clearer on the phone. I asked his teacher and she said it's because he can hear himself and that helps a lot of kids. She said they will assign him a little take-home phone when he starts school next year if I like but that I can pick one up at Lakeshore Learning for $4 to use over the summer and it's THE SAME ONE. Guess what I'm getting after we pay bills!
Well, sorry this took so much space to write, but I'm passionate about speech pathology, now, and there is so much involved in getting the process started to get your child help if she needs it. You know her best, if YOU feel she needs, she probably does, and if she doesn't then you can rest having taken that pressure off.