First of all, we have a pediatrician in Belize.
Second, the purpose of the volunteer law to to keep well meaning volunteers from taking jobs from Belizean citizens who depend on the work to survive. If it can be shown that there is an unfulfilled need, immigration can be open to writing a letter that allows a temporary work permit. We have done this at the library.
In terms of medical work, the medical board must approve local licensing to practice just like your federal and state licensing board in the states.