http://election.dos.state.fl.us/online/faq.shtmlRegister before you get a Florida DL. (BTW, they have an online reservation system for the Florida DL, it's much better than in the 1980s, the last time I lived in FLA, in and out of DMV in an hour. Not your primary concern, but if you do get the DL, at least it's quicker). When you register, use your SSN as your identifier.
When you vote, use one of the forms of ID on the website above. I suggest a photo credit card, which is valid ID, unless you're lucky enough to have a passport, neighborhood association ID, or student ID. Be ready to quote chapter and verse about the validity of the card when the pollwatchers strike back.
I'm not positive, but it appears that gender is an optional question on the Florida voter registration form. The form says what parts are required, and that's not one of them.
Call your county dem organization if you have questions, or I can try to get some info for you (although I'll be offline until July 1st after tonight).