You could try Ft. Desoto state park in St. Pete. There may not be any reservations, but they leave spaces for drive ups. In that regard, you'd have to take a chance. We live in the Orlando area and Ft. Desoto is one of our favorites. Many campsites have water views and you can take a couple minute car ride to beautiful beaches. You can also ride your bikes on the paved trails to the beach. The tough thing about camping in Florida in the winter is finding a nice place that's not booked. On the other hand, if you are camping at Disney, you won't be disappointed. It's fantastic. Pricey, but great. Enjoy.
2012 F-150 Lariat, Ecoboost, 3.73, Max Tow Pkg
2013 White Hawk DSBH
Equalizer Brand 10,000 lb. WD Hitch