I am the mother of 3 and one is in a gifted program now and has been for years, the 2nd will soon follow suit, the 3rd is talking way more than they ever did at this age.
DONT WORRY would be my advice. Unless you plan to push them through trying to get them to be doogie howser, graduated at 16 and already off to college then I wouldnt worry so much. And personally I dont want my kids out of the nest at 16 or exposed to HS at 10, etc They may academically be ahead and even be mature for their age but socially are they ready for the pressures of teenage or adulthood earlier??
OK now off my soapbox and to tell you what you can do. Follow the childs interests, if she shows an interest in reading and WANTS to learn, teach her (I like Ready to Read Ready to Count handbook, available at RCPL or for order at amazon, etc) as it makes it fun, they are starting to read in only a couple lessons so feel accomplishment and doesnt push), if she wants to learn why she burps get a book about the digestive system, etc etc But otherwise just let her be a kid. Being a kid and learning daily living skills, their address, their phone #, bday, parents name, emergency info, what to do in an emergency, how to make believe, relax and have fun is so important as they will be pushed into academics so fast once school starts. Very few public or private schools do not teach reading in K so if you push your child to read now she will be repeating it at least some of the day in K (GOOD teachers divide the kids into groups and work on their level so they will learn in K but a lot of the day is still as a class) as with many other things you could push now.
Also keep in mind that most kids level off around age 6-7 so the gifted child will be identified more by the WAY they think not by what they know. An average child can be pushed to learn too much and a gifted child can relax but that wont make the average child gifted or the gifted child not. A gifted childs critical thinking skills are different and it shows in how quickly they pick something up. You see it come elementary school when an average child progress 1 yr of reading levels in 1 school year but a gifted child progresses 4 years in 1 yr (as happened to my 1st 1 yr). Or when they are just introducing certain math concepts, not expecting mastery but the gifted child does master it.
You do NOT want to burn a child out and qualch their love of learning as that will hurt them in the most important academic years when it comes to future (transcripts, college admission, etc), their high school years. So you have to keep learning fun when they are young, fun and relaxed. I have seen good teachers able to spot a gifted child in only 5 mins of conversation, none of it academic. You just have to be there to make sure the child is getting what they need from the school and teacher when the time comes so they dont get bored or complacent. My children have gone through the 2 best school districts in the state and neither has needed special training at 2, yet both have managed straight As