You aren't too late (except for waterfront state parks in the Keys that fill up the second bookings open, 11 months ahead. Even there, you may pick up some days here and there, by checking the websites often, or by showing up next winter and asking about cancellations.)
Don't forget county parks with campgrounds. There's one called Long Point in Melbourne surrounded by the Indian River, for example. One popular one is Ft. DeSoto, below the Tampa Bay Area. Some county parks give first crack at booking to their residents, then open up res to others.
For commercial parks, you may find they have been concentrating on rebooking their regulars who come for the season, and now are filling in with the shorter stay two-week type returnees (like us.) So it's good you are thinking ahead now.
Fishing is available almost everywhere in Fla on lakes, rivers, offshore, etc. You might like the "Treasure Coast" area below Melbourne Beach. Lots of fishing around Sebastian Inlet State Park, which has a popular Campground. I enjoyed the McLarty Treasure Museum near there.
Enjoy!