We took DD3goingon23 to Chef Mickey's. Yes, it was a little wild, and before we were seated, she got a little spooked by Goofy. Looking back, I don't think I would go to Chef Mickey's as a first character meal.
Don't get me wrong -- she loosened up, thanks to Chip and Dale, and by the time Minnie came around she was ready to do her hoochie-mama dance! She ended up loving Chef Mickey's.
We also did the Princess Breakfast at Norway - which is not a non-park event, but similar. She really loved that one. It was quieter, the featured attractions were real people instead of characters, etc. Had a ball at that one.
By the last event - Pooh and Friends - she was a pro!
Bottom line -- I would definitely go to Chef Mickey's because of the characters present, but I would ease her into it by going somewhere else first.