Here's an interesting link for places to take your dog (some have dog swimming areas) I'm not familiar with all the cities but they seem to be all on the coast. PEAR Park in Leesburg supposedly has a swimming area for dogs.
Florida Dog Parks - Doggeek.com
Here's a link to a place in Ocala that has a public pool for dogs.
Millennium Dog Park
I don't have a dog, so I can't recommend anything, just passing on some info.