Insurance for newborn

Ok I need help! I’m currently under my mom’s insurance because I’m under 26 and not married. She has blue cross blue shield which covers my pregnancy. I need to find my baby a pediatrician but I don’t think my mothers insurance will cover her as well. How do I get insurance for her. I’ve been trying to see if I can pay monthly but every where I look it wants to put me on the insurance as well. Her dad does not have health insurance yet but is looking to get some. Is it best to just let her under him?