If your location is IND as listed on your profile, then you could drive to Destin in a total of 12 hours. Leave a day early, drive 7 hours to BHM. Day two, drive the last 5 hours. Fares in and out of BHM are generally pretty low, might only cost you the change fee and a tad more. Or, you also think about BNA.

And while some might call it heresy, you could also check the same airports for Southwest flights. From LAS you could find non-stops to SDF, BNA, or BHM.