You guys worry about the strangest things. Here in Florida with alligators being protected they are in just about every back yard pond that you can find. On my morning walks I ocassionaly encounter them and they are usually very shy and non agressive. Even if you were to fall into a pond with a gator present unless you are just unlucky, the correct size, had the mishap to encounter one that had not eaten for a week or so, nothing would happen. During mating season they tend to be more agressive and on the move. The chance of a reptile eating your dog would be a pretty big longshot. If I would plan on taking my dog I would be alot more concerned with the various diseases that the animal population of AC harbors. Your dogs are more likely to be accidently posioned than to be devoured by a gator.
Be more worried about those fast talking, two legged sharks that inhabit Belize.
I would scratch this off my list of worries about Belize.