I suggest you use VRBO.com (Vacation Rentals By Owner).
You can do a search on the specific area and use the filter to include Pet Friendly. I have used them many times, this site has a very good reputation. I do know the Hampton Inn in Fort Walton will take pets (we stayed there once before finding VRBO).
Also you can check out the website
www.BringFido.com , they have listing by area.