St Simon's Island, Georgia. I spent a week there, after Labor Day last year and its legal to have dogs on the entire island including the beaches if on leash. Actually they seemed to be pretty lax on the leash law on some of the beaches. Hotel was easy on dogs too. We took my old Rottweiler and my sister's Shar Pei. Pretty nice place, half way between Savannah and St. Augustine if you want some other diversions.
I think our forum member by the name of AHP lives on the island, might be worth getting a hold of him.
My experience has been that nowhere on the panhandle of Florida is dog friendly. Gulf Shores and Orange Beach aren't bad as far as hotels and in the towns but not on the beach.
Simpler is better, except when complicated looks really cool.