LOL sorry your post got hijacked zing..
Many people have travelled to BZ with their dogs.. Here is an old post
that has lots of details.. You can follow up accordingly to confirm if things still are the same.
Not saying your dog needs a passport, but certainly does need documentation. Keli (I Do Belize Weddings) may not be in BZ at the moment but probably monitors the board and can assist. Swanno may be able to help.
Best of luck.