You do not have to leave your pet at home as there are many pet friendly places where they can stay with you. There are beaches for play and dogs are allowed at the Ding Darling Wildlife Refuge but they must be on a leash and cleaned up after.
It is suggested that you call before your visit to the place you will be staying to verify that the accommodations is still pet-friendly. Policies and the management are subject to change. Also check with them as to the breed and size of dogs they allow at their facility as some allow all sizes and breeds and others just small dogs. Better to be safe than sorry.