Unfortunately, this depends entirely on how things go with the baby and the delivery. If baby is healthy and Mom isn't recovering from a C-section, they would probably be just fine. However, if there are complication, she or the baby might not be up to it.
FWIW, we took DD for her 1st trip at 6 weeks, just before I had to go back to work. Both of us were fine. I carried her (and nursed) in a sling all over the place, and I just rested when I felt tired. This was in early September, so it was hot, but we kept ourselves well-hydrated and used lots of sunshade mechanisms. (DH took an adorable pic of the two of us snoozing in the shade at Blizzard Beach.)
If you want to buy air tickets, I'd advise purchasing them on points on SWA if at all possible, so that you will get a refund if they don't feel up to the trip.