Yes, unfortunately, there are no NICU specialization programs (I wish there were! A simple course would be nice!). I've checked into UF myself (for my BSN), and I know that they have access to Shands Hospital, which is a very large, well-reknowned facility where you're sure to get a lot of good clinical experience.
I doubt that there's a need for you to move out of state (unless you want to!); Florida's nursing programs are just as strong as the others (it just depends on the school, not the state). Later, when you are looking into a Master's degree (or, I should say "if"), the school itself will make more of a difference (some MSN programs are stronger than others in certain areas of nursing).
Check with the Florida student nurses' association and the Florida state board of nursing to find out statistics on NCLEX pass rates and graduation rates (the NCLEX is the test that we take in order to get a nursing license after we graduate). Ask nurses you know or other students in the programs about their school and get some opinions to weigh. Call the nursing programs at a couple of schools and ask if they can put you in contact with students or graduates that would be willing to answer questions for you. Go on tours of the nursing programs and ask lots of questions! This is all stuff you can do while you're still in high school.
If you really want a head start, think about volunteering in an NICU, pediatric hospital, or other medical area that works with children. This will make you a stronger candidate when the time comes to either be admitted or after graduation when you're looking for a job (because you'll have more exposure to pediatric/neonatal healthcare and have more realistic expectations). You're a junior in high school- you don't have to commit all your time; how about once a week or twice a month? Just do it on a regular basis so that you can build up a rapport with the people you're working with, and then you'll have a reference from them when you are trying to get into/out of school.
Good luck!
Also, since you're interested, check out the book "Baby ER" by Edward Hume; it gives you a really good look into the neonatal unit.
Let us know if you have more questions! Good luck in school, and remember- enjoy the time you've got now. All of that responsibility will come on its own. Good planning is wonderful, but don't get obsessed about it. You've still got time.