My husband stuttered very badly as a child. Come to find out, it was something with his ears. They put tubes in his ears and some speech therapy at school and he stopped.
You could talk to a speech therapist about it too. My daughter was in speech therapy (not due to stuttering) but I'm not sure if it works the same or not. We just called All Children's Hospital and they did some testing on her and she qualified. We did not have to pay anything out of pocket. At age 3, you can put her in the pre-k program through the public schools for a couple of hours a day where they work on speech through playing, crafts, etc. Or you can just take her twice a week for 30 minute sessions while you wait. It's up to you on which you would go with if you qualify.
Or it could be something she outgrows. Personally, I'd go ahead and try with All Children's. They may say it's not bad enough that she needs therapy. If she does, it's something you can take care of now rather than later.