Insurance for kids?

My family's health insurance is through my job. Once I'm done with maternity leave, I'm going to be getting a new job and I have to wait 3 months until insurance kicks in. Having a newborn and no insurance makes me really nervous. I'm trying to google it and ending up with more questions than answers. Is there some sort of state/government insurance I can put the kids on for 3 months? I'll have a 2 year old and a 3 month old. I'm not worried about myself or my husband, but I don't want the kids to miss their routine visits just because I started a new job. We make a good living and have never needed state insurance before, so I have no idea what to look for. I'm in Florida if it helps. Thanks in advance!