I think with wedding/prom hair, there’s a HUGE expectation attached to the event so you really need to be on top of your game in terms of creative styling as well as confident enough to handle difficult, bridezilla type clients.
It’s not that difficult to imagine a child bridesmaid (or even a fussy adult) moving suddenly and getting a burn when you’re curling their hair with a hot wand, so good insurance cover is essential. For insurance purposes, you normally need to prove competency so I would expect some form of hair styling qualification, although they might accept attendance on a specialist wedding hairstyling course, but you’d have to check with the individual insurance company.