No minimum age requirement!
This is one of our favorite things to do in Disney. We learned, in January, that you do have to arrive pretty early to be guaranteed a spot in the next show. For example...let's say you arrive at 12:20 for the 12:30 show. There will already have been people lined up prior to noon even for that 12:30 show. They have a line and a holding area. The holding area is where people from the line are let in and those people get to go into the next show. They usually fill that holding area right after they let people in for the prior show (so for the 12:30 show, they would have let people in to the holding area at noon). If you don't make it into the holding area, you have to wait for the NEXT show which would be the 1:00 show in this case. We ended up discovering we usually had to wait for one show to make it in (so if we arrived at 12:15 for the 12:30, we would have to wait for that 12-12:30 show to finish, then the 12:30-1 show to finish and then we'd make it in by 1).
Sorry if that seems complicated! It surprised us that we had to show up earlier than we were expecting. It is so worth it though! We were even there in January so it was a slower time and we still found we ended up having to miss a couple shows due to ADRs because we wouldn't have made it in until 45 minutes later PLUS the show is a half hour. It takes a chunk out of your day for sure. But a very worthy chunk!