Our dog has never been happier. She loves it and we have picked up two more since we've lived here. Be very aware of the symptoms of tick fever (erlichiosis). Many expats I know who have brought their dogs from abroad have experienced this with their dogs. Ours caught it soon after getting here. Some info is here http://www.familyvet.com/ehrlic.htm
At the moment there is a full time veterinary surgeon on the island, although the surgery is very basic as it is run by the local animal welfare group, SAGA, who don't run it commercially. //ambergriscaye.com/sagasociety/ . There are better equipped facilities on the mainland if necessary.
Many households have one or more dogs here. Your concept of pet keeping may be different to many who live here though.
It is very dog friendly here. Dogs visit many restaurants and supermarkets with their owners.
There aren't too many dangerous critters on the island in terms of dogs except for crocodiles and mosquitoes, which of course carry heartworm - so make sure you get yours on heartworm preventative treatment before you come.
We are not liberal parents to our dogs as Elbert is to Bubba and we don't allow them to blog as they would probably air our dirty laundry in public. But we do write about them on our own blog http://exploringbelizecontinues.blogspot.com/2008/07/blog-gone-to-dogs.html