I've never heard of anyone who had their pets quarantined upon entry to Belize. Like someone said, so long as you meet the requirements for rabies vaccine, import permit, and certificate of health, once BAHA inspects your pet (in our case, about a 5 sec. look over of our dog at the airport), you pay your fee and are on your way. They certainly never said a word about not going outside or mingling with other dogs for 30 days. Just follow the rules, and you'll be fine.
For non-pet animals (i.e., farm animals and the like), the rules are likely more stringent, but for domestic pets, it's quite an easy process.
As stated above, Melanie Robateau at BAHA is very helpful. We did everything through email and fax and never had to make an international call.