Disney traps gators over 4ft long and relocates elsewhere on property away from guest areas. They do not destroy them.
Fl Law is pretty strick where gators are concerned. In fact, it's a good thing you didn't hit the gator. FL law protects the gator and you could have been in trouble. Per FL law there is a Nuisance Hotline where you can report problem gators. IF they determine the gator is a problem then a licensed trapper will be sent out to relocate the gator. However, just seeing an alligator does not classify it as a nuisance.
Like an earlier poster already stated Floridians have a saying "If there's a puddle...there's a gator!" However, to all of you coming here on vacation do not in anyway let this scare you! Gator attacks are actually very rare when you consider just how many gators are out there and how many people are in our lakes and rivers everyday. I'm sure that wherever you call "home" there are some dangerous animals (snakes, spiders, bears, etc) that share it with you, but I'm pretty sure you all leave your houses everyday. Nature should be respected, but not feared.