Like Gwen I dealt with BAHA by Email and phone. I applied for a pet passport which costs a little more than an import permit. Get the forms by sending an email to BAHA. I provided them with a health certificate and a current but more than 30 day old rabies cert. They emailed me that the paperwork would be waiting for me at the airport. I emailed back that I needed a copy of it for the airline and they complied. I also kept all of my email correspondence to and from them.
When I arrived in Belize, no passport waiting at the airport and I was delayed slightly at the BAHA office but I insisted and had the proof with me. It was a Saturday so BAHA was closed. They eventually let me through with no extra fee and told me that my passport would be sent to me. Monday I emailed BAHA and they sent my dog's passport out via Tropic. I just had to pick it up at the airport for an $8bz postage fee.
Moral- keep all your correspondence (for the airline and BAHA). I now have a large brown envelope which will accompany while traveling back to deal with whatever? At first it seems very complicated but it isn't and it will work out. Be sure to comply with all the airline's rules because that is probably worst for a first timer than dealing with BAHA. Others have told me there are slight variations with each trip. Good luck.
PS I used Continental and they were great but a little expensive. My dog received VID (Very Important Dog) status on the whole trip and there was a van right there (one with paw prints on it) to pick him up and to deliver him to the connecting flight, all in a controlled environment. (it was 10 deg. the day we left) We witnessed the whole thing except the loading at Logan through the airport windows. It came out to about the price of a seat on board because he weighs 58# plus the kennel for the flight. Although my wife had doubts about the whole deal and suggested strongly that he remained up North with our kids she now agrees that it is a joy to have him here. I’m glad she finally gave in because I would have missed her, she is a good wife.