The vet procedures are every day and are around 9-11 AM at Rafiki's Planet Watch Conservation Station. I suggest to get to Animal Kingdom as early as you want, check at Guest Relations for what is going on that day, then head back and see the entire Planet Watch. If anyone is into animals and wants a future in that area, it's a wonderful place. But, you will have to walk back to Africa, the way back Africa to get on the train to go out to Planet Watch and then walk a trail (that has exhibits) to get to Conservation station.
Once there, all of the Cast Members are willing to talk about the animals that are there and will even talk to the "audience" during the vet procedure. The procedures are behind glass but anyone there can see the "operation".
Disney not only cares for the animals in the theme parks but also animals just on Disney grounds. We watched as a turtle was having his shell repaired because a car ran over him at the Hess station near the Boardwalk. We were told the turtle would remain with Disney until it was determined the turtle could safely survive on his own and then be released back where the injury took place in the hopes he could find his way back home.
Disney also does yearly exams on all of their animals so it might be a routine check up but even those are interesting. We had just missed a warthog getting his teeth cleaned.