is it possible to travel with a tiny dog from the U.S. to Belize?

Micki,

Vist this page for details: http://www.customs.gov.bz/traveller_info.html

Summary:
For passenger who intend to visit with pets:

A) In the case of dogs and cats, passengers are required to present the
animal's most recent health and vaccination certificate. Obtaining a permit for these pets from BAHA is the same as is described above for obtaining a permit for ham or turkey.

B) In the case of monkeys, passengers are to obtain a Cites (a special permit which comes with a letter stipulating conditions) from the Ministry of Natural Resources (under whose umbrella institutions like Belize Audubon Society fall). A permit from BAHA is also required and passengers must present the monkey's recent health and vaccination certificates. Remember that these permits must be obtained before hand in so as not to delay the clearing process. Links and numbers to important Government department and ministries will be provided below.

C) In the case of birds, passengers must provide a Cites from the country
of origin along with its health certificate. A permit from BAHA is also required (obtain before arrival). Note that these permits will specify whatever conditions the passenger needs to satisfyy before importing their pets or items. Note that BAHA will not allow any birds to be imported from Mexico. However, passengers passing through Mexico to Belize with pet birds will be allowed to import their birds providing they present BAHA with the documents aforementioned.