Hi, musiclover!
Welcome! First of all, congratulations on doing research - here you'll hear the good, the bad, and the really nasty stuff. Yes, there are bad things that can happen, but my research over nearly a year has indicated to me that the good stuff far outweighs the negatives. I'm hoping to get my surgery done this summer.
With regard to gigging - I play woodwinds, and I play in pit orchestras as often as possible, as well as the occasional other gig. I haven't had THIS surgery, of course, but my experience with other abdominal surgeries (three of them - one open abdomen, the other two laparoscopic) is that because of the pressure on the diaphragm and the abdominal muscles, I would probably give it a month to 6 weeks before I tried to do a full weekend gig. I actually did a pit orchestra gig (4 nights a week) 5 weeks out after one surgery which had me back in rehearsals by two weeks after surgery. Luckily, I was working with a group that had worked together often, so I could take it pretty easy and not push it - I mostly played anything where I was exposed or a cue for someone else in the pit or on-stage, but rested a lot of the rest of rehearsals, and I was still pretty worn out. I didn't really play full-out until the week of dress rehearsal and opening (4 weeks out), and even that was tough. Knowing what I know now, I wouldn't start lightly practicing until about 3 weeks out, and probably wouldn't take any gig longer than a night until 6 weeks out, but everyone heals at different rates, and you may have more energy earlier.
Good luck!