The real question to me is where in Destin are you staying? Because there are a couple of routes in and just moving 5-10 miles in either direction can change the recommended route.
If you are staying on the eastern side of Destin, then my recommendation is...
1. I-85 south from Atlanta
2. I-185 south
3. Exit on hwy 80 west to Alabama
4. Left on 431 south (make sure to follow 431 all the way to Dothan)
5. 231 south out of Dothan
6. Turn right on 273 at Campbellton
7. Turn left in Chipley at hwy 77
8. Follow to I-10 west
9. Exit on hwy 331 south
10. Right on 98 to Destin
If you are closer in to Destin, you might want to avoid 98 some and take the Mid-Bay Bridge in.
In that case pick up at 9 above...
10. Turn right at hwy 20 off 331 south at Freeport.
11. Turn left on 293 and cross the bridge in to Destin.
BTW, I was on I-85/I-65 through Montgomery last summer twice to go to Pensacola and I had no issues with the roads.