I'm not really sure on a couple of your questions, but I would advise, if this class is as hard as it's supposed to be for the Navy Nukes, you might want to wait until she is finished before putting the added stress of being a newlywed on her plate for the time being. If you both love each other as you say you do, you can surely wait a few more months.
As far as base housing. Unless it's a permanent duty station, I don't think you qualify for the housing. Somebody in the navy might be able to answer this better than I can, since I was in the army, but that's the way it was there. Also, with the economy being the way it is right now, the base housing will probably be pretty much full, since you don't have to pay for all the stuff on the economy at an apartment or rental house, such as electricity, etc.
I'm not trying to discourage you, but you might want to really weigh your options before you jump right in. Another thought for you, have you thought about what you will do while she is in school? Are you going to college down there, looking for a job, etc? An E-3's pay is not that much and heaven forbid if a pregnancy got involved. I knew many E-4 and E-5's that could barely make ends meet with a mortgage or rent payment and car payments.
Stacey