The rules might have changed, but when I had my first, five and a half years ago, the doctor I wanted for my daughter told me that they weren't accepting new medicaid patients. However, he also explained a loophole to me. If a doctor sees your child in the hospital, you are automatically considered a new patient in the practice, you're "born into it," per se. You can tell the hospital the name of the pediatrician you'd like to see your baby and they will accept her insurance...that is, if they accept medicaid at all, actually. Some offices will not accept medicaid, but if they do and are just not taking new patients this is a good way to get in anyway:).
Go to the office you would like and schedule a pediatrician interview. Come with lots of questions and you'll have the doctor's undivided attention. Ask if he/she would mind if you requested them at the hospital.
Best of luck and congrats on your new little one!!!