I've paddled a ton in Florida and had some minor run-ins with alligators...most involved the gator swimming under the boat, getting freaked out, and thrashing a little as it swam away. It makes your heart go a bit fast especially if they are bigger than your canoe or kayak, but the only really dangerous thing I ever saw was a tourist couple who paddled up to a LARGE male alligator during breeding season and it charged off the bank and hit their boat. They were fine but I'm pretty sure the guy had peed himself. I wouldn't worry about it...but maybe don't splash around a ton if you think one is right under the boat. They evolved to catch smaller prey like raccoons, birds, small mammals...they will grab deer and people occasionally but its pretty rare. Check out the Peace river while you're down there...fantastic trip with tons of cool fossils in the riverbed, great scenery and wildlife.
Vanessa (not mbannister