The important thing is to be aware of the seasonal embargo on flying pets. We had to change our travel dates when we moved here with our dog to enable her to fly. We flew from London to Atlanta, where we spent a week or so. We flew with Delta and took the direct flight to Belize City. As long as you have all your papers, getting through is pretty easy. Just make sure you contact BAHA to get all the information you need on the paperwork.
We stayed with friends on the mainland for a few days before flying her to San Pedro. We broke up our trip in this way as it was such a long journey for her from the UK, we felt we had to give her breathing space in between flights. We paid for three seats for her on the Tropic Air plane so that she and her crate could travel. That was the most expensive part of the journey. Check with Tropic or Maya and give them the dimensions of your crate, so that they can tell you what you will need to book to fly to San Pedro.
The water taxi is another alternative and won't cost you as much to go from the mainland to San Pedro with your dog, but it takes longer and you'll need to find a taxi driver in Belize City that will carry your dog from the airport to the water taxi.