I can't remember the process, but I do recall it was easy to get beach premits for our dogs on their trips. Seems like I went to the South Walton Chamber of Commerce website and find links to the process. Dogs wear their permits with pride. But, yes, do have your dogs permittted.
You can also call the TDC (800) 822-6877 and request a vacation planner. It includes a huge listing of rental companies and private homes. There's a little doggie bone next to pet friendly accommodations.