I recommend you sleep at night and find a hotel after 12 midnight.
Route: I recommend I-20 East to I-55 South to I-12 East to I-10 East To Florida Highway 87 South to Navarre.
"OKALOOSA ISLAND" Something To See
If you've got help driving and want to save some time go I-20 east to Jackson MS and then take Highway 45 South to Biloxi, Mississippi, and then I-10 east to Florida Highway 87 South to Navarre.