Dave: I've done that trip many times but mostly IFR. It is busy airspace and I highly recommend flight following at least from Mobile east. When I file from here (Addison), its the DP to Alexandria, to mobile, then direct. There is some restricted airspace around Alexandra and just west of Mobile you'll need to stay clear of.
The controllers usually take me south over the water between Pensacola and Destin. As has been said Eglin is great to work with. I'd really study the charts from Pensacola east and make sure you know what's what, but with flight following or IFR they should direct you pretty well. The only issue with flight following is they can drop you and if they do, you really need to understand the airspace well. There is a lot of military training west of Destin and over the water to the south. More reason to be talking to the local controller.
Have a great trip. That's one of my favorite places. Since they've gotten the second FBO, pricing has gotten a bit more competitive. There was a fuel discount on weekends last time I was in and I was able to negotiate a bit on the rental car.
Best,
Dave