For two-legged threats and gators, a .44 should do the trick, but my preference would be a good .357 magnum 4-inch in a pancake holster and stoked with 125-gr. JHPs. Gators are most dangerous up close and a heavy .44 is heavy to carry and doesn't point and shoot in close and as instinctively as a good .357 -- plus recovery from recoil is longer.
If I carried a .44, it would sport a 4-inch barrel and be downloaded a bit with perhaps a 180-gr. JHP/JSP.
I hate gators. They're dangerous, ugly, and have no personality. Three-fifty-sevens also pack more punch into a single shot as far as people and critters that size go and don't overpenetrate like .44 mags do.
The Smith 66s and Ruger Security-Sixes were just perfect for this kind of packing. Just my opinion, though.