New FL guy here, not new to hunting or airguns

Does anybody have any information on the laws and where to go on the Treasure Coast of FL to hunt small game like squirrels with airguns? I go hog hunting on private land, but to go strictly rodent hunting on public land sounds interesting.

I had an American made Daisy 880 back in the early 1970s and it was excellent. I could shoot a wasp off a milk jug at 25 feet.

Also, what do you think about keeping a full-auto BB pistol as back up to a rifle? I like break barrel, pump or CO2. I am not into the SCUBA tank unless I am going diving.