From the Florida State Parks website
Welcome to Florida State Parks
For everyone's enjoyment, including pets, please observe the following pet camping rules. Failure to abide by these rules may result in the camper being asked to board the pet outside the park or check out of the campground.
Pets are not allowed in any state park cabins.
Pets must be vaccinated against rabies. Owners are not required to show proof of vaccination.
Horses must have proof of negative Coggins test.
Pets must be confined, leashed or otherwise under the physical control of a person at all times. Leashes may not exceed six feet in length. Pets that are tethered at a campsite cannot be left unattended for more than 30 minutes. Pets may not be tied to trees, bushes, tables or shelter facilities even when the owners are present.
Pets must be well-behaved at all times.
Pets must be confined in the owner's camping unit during park quiet hours, 11 PM - 8 AM.
Pet owners are required to pick up after their pets and properly dispose of all pet droppings in trash receptacles.
Any pet that is noisy, dangerous, intimidating or destructive will not be allowed to remain in the park.
Non-furbearing pets, such as reptiles, birds or fish, must be confined or under the physical control of the owner. Some animals may be prohibited on park property. Captive wild species, whether native or non-native and barnyard animals, except horses, are prohibited.