AL deer season just ended, lots FL hunters head west and north a short drive to hunt Corps of Engineers Land along the Tombigbee River, as it flows into Mobile Bay.
Try Blackwater River State Forest to the Northeast a short drive, the biggest state forest in FL. Federal land such as that surrounding the naval base sometimes offers some hunting opportunities if you can get access, and private land abounds. that's your best bet, pick up a lease on a private timber tract, more trophy potential.
try Craigs list for hunting clubs for lease in the area, and post something saying you are looking for land to hunt/ lease. follow all regulations. as already stated. dog hunting is not always smiled upon by still hunters, or adjacent property owners when the dog strays across a line.