I have cruised with Carnival a lot and have had that last minute cruise fever a few days before a cruise. If you are serious about cruising on the Destiny(nice ship) then I would indeed call carnival asap and ask to be put on a waitlist. If again you are serious you can offer to put down a deposit showing you are a serious inquiry. A lot of times you will get that magic call and your on the ship.
But if you are flying a ways to miami then for your airfare especially last minute may cost you a nifty penny.