I have never been to Caye Caulker but we moved to San Pedro at the beginning of December and after a bunch of shots and finding an airline that would bring her (Continential) we had our St Bernard join us on Feb 4th. Naturally she dwarfs all but the big guard dogs but we have found no instances of people being afraid of her...they want to fuss her and take her picture but no machete weilding madmen. As Libra said though make sure that you keep your pet on a leash instead of letting it run wild. As far as temperature goes...it isn't much hotter here than it is in summer where we were in Canada and basically a large dog can have a very happy life here hanging out inside sleeping in the day and exploring with you at night...I'm sure that Shmoo (our dog) would write a review of how much she loves the Caribbean breeze and the scents it brings but her paws are too big for the keyboard. Do make sure that your pet has taken heartworm meds though as it is a prevalent problem here as are canine stds so while you want your dog to enjoy him/herself make sure they don't enjoy themselves *too* much lol.
Once again as I said I haven't been in Caye Caulker yet but Im sure that the canine sensibilities can't be that different between there and Ambergris

If we give Peas a chance won't the Lima Beans feel left out ?