Here are some odd animal laws from around Fl., don't know what animals are banned though.
Big Pine Key
It is illegal to molest a Key deer. If caught one will be fined or will have to go to jail.
Key West (also my favorite, but applies to only the Gypsy chickens that are wild)
Chickens are considered a 'protected species'.
Sarasota
You may not catch crabs.
Hialeah
Sec. 3-1. Bird sanctuary declared. (a) It is hereby declared that all territory embraced within the corporate limits of the municipality shall be a bird sanctuary. (b) It shall be unlawful for any person within the municipality to shoot, trap or in any manner kill, wound or maim any bird of any kind, or at any time to throw at any birds of any kind any missile with slingshots or any other weapon, or to disturb their eggs or their young or their nests. (Ord. No. 8-59, §§ 1, 2, 8-10-59)
FL wide
Doing the deed with a porcupine is illegal.
If an elephant is left tied to a parking meter, the parking fee has to be paid just as it would for a vehicle.