In Okaloosa County, animals are prohibited in "county" parks, beaches and other recreational areas with the exception of service animals or K9 units. 

Here are some dog parks in Destin or surrounding areas:
https://www.ecvr.com/blog/2015/5/dog-parks-near-destin

http://www.cityofdestin.com/Facilities/Facility/Details/9

https://www.bringfido.com/attraction/parks/city/destin_fl_us/