Mathew, I think that you and your wife are in for a wonderful experience.
It sounds like you have some flexibility time-wise. You might want to plan your visit to coincide with some major events. First, of course, is Mardis Gras (and the week leading up to it). Or a little later you could easily fit Festival International, Balfa Camp, and Breaux Bridge Crawfish Fest into a couple of weeks. There's also Festivals Acadienes et Creoles in the fall.
Also, make time to enjoy Louisiana's unique natural environment (or what's left of it). Take a tour of Lake Martin when the birds are nesting. Stay in a houseboat for a few nights on Lake Henderson.
You must take dancing lessons if you don't already know th dances!
You'll love it!
If you have no experience with the instrument yet, I would suggest attending a music camp first (Balfa Camp for instance), learn with some other players, then scope out the local scene while you're there. THEN take a year to get better on the instrument, and THEN do your sabbatical to Louisiana.
If you're spending your whole time struggling at a beginner level with the box, it might not be the best way to go. You might feel overwhelm trying to cram a bunch of learning in while you're there, and frustration from the pressure.
If you're already an accomplished musician and pick things up easily, that's another matter.