First - search this forum for a couple of older threads on becoming an NNP. There's a lot of good info in there!
But in a nutshell - here's some basic facts. Most NNP programs will only accept you AFTER you've had at least 2-3 years of clinical experience in a (level 3) NICU as an RN first. While you learn a lot in nursing school, most of it deals with adults. As I'm sure you learned with your daughter - premature / sick babies are a whole different ball game compared to adults (even compared to children). During those years in the NICU as an RN, you will learn tons. The bedside nurses in a NICU are the eyes and ears of the unit. Also during this time, you can see the different roles played out by the bedside RN and the NNP. This would be a great time to shadow an NNP as well (you can also shadow an RN or NNP during school!)
Some NNP programs allow you to go to school part time, that way you can still work shifts as a RN on your unit as well. Check into the programs in your area. There's a nice "stickie" on this forum that lists NNP schools by state.
Hope this helps and good luck!