Baby Insurance!

I am a very lucky girl...I am still covered by my step fathers health insurance until my 26th birthday so all of medical costs during my pregnancy will be covered by that. However, because I am a dependent the health insurance company will only cover the baby through delivery. Meaning that I need to have health insurance set up for our little one before giving birth.
 This seems like it would be a pretty easy task right? Wrong!!! I have looked up a lot of very afforadable health insurance programs, that would be a great fit for what our baby will need. The problem is signing up for these programs so that the baby will be immediately covered once I give birth.  In order to get insurance for a child I actually need a name and birth date, which I don't have yet, because MY BABY IS NOT BORN YET!!!!
The websites I have visited so far say that the baby will be covered by the mothers insurance for a period of time after birth, but in my situation...with my insurance the baby will not be covered at all once delivery is over. I need to have insurance set up in advance in case there are any complications (I am hoping there won't be).
I know I am only half way through my pregnancy but if you know me, you know that I am a planner and I do not like the unknown, so I am wanting to get things set up as soon as I can so I have less to worry about in the days prior to the babies birth. I am just starting my search for all of this so if any of my readers out there know of any places to look or what the next step should be, please let me know!