I hunt on private land, so I can use whatever gun suits my needs, as long as the caliber is legal. When hunting in state and federal designated areas, you have to follow the rules specific to that area.
In Ocala, and other state wildlife management areas, they have a "Small Game Season" during which you cannot possess a centerfire rifle while in that forest. You can only hunt small game with rimfire or shotgun.
In Ocala, coyotes can be taken during "General Gun Season" from November 14th to January 9th, and bobcats from Nov. 20th to January 9th, all with centerfire rifle. Then "small game season" starts January 10th and runs until March 6th. That's when you can only use rimfire or shotgun. There is an "extended fox, bobcat, rabbit, & raccoon" season starting March 7th and running until April 17th. You can hunt only in the Pipeline Unit west of hiway 19, and south of hiway 40. One other rule applies during the extended season - possession of guns is prohibited. So I don't really know what you use to hunt with during that season, maybe dogs.
You'll need your regular resident hunting license, and the wildlife management area stamp. You'll also need a lot of bravery and luck if you go into Ocala during general gun season. I stopped going during that season back in the early 1970's. I only go during small game season. Still, during the 2002 small game season, when 3 of us returned to our trucks after a day in the woods, one of the guys trucks had a centerfire rifle round stuck in the top of the cab. Someone had fired their rifle in the air, perhaps a mile away, and the bullet came down and stuck in the top of his truck, going halfway throuh the metal. I read in the news each year about people being shot off their deer stands, or mistaken for turkey or squirrels in Ocala during general gun season. Make sure you buy camo hankerchiefs! I'm serious - never take a white hankie out and blow your nose with it in Ocala. You'll be shot for a deer!
Good luck!
TennSquire