I'd say a 9 year old L4 is fine, but I'm not the one who needs to be satisfied with respect to level and age. You dd may have an opinion based on where she'd like to be two years from now. This fall as an L4, and the following season at L5 will set her up for a possible move to optional work by age 11 or 12. Learning that kip as soon as possible is a big deal if she has that same schedule in mind.
Another concern is how the gym defines itself by the kids they want to move up a level when they see two kids with similar skill sets. The younger child is generally regarded as the more attractive choice because she'll have more time to work up to more difficult skills, and younger kids tend not to get overly concerned about a skills difficulty or risk.
So yeah, I'd be happy to have her as a L4, but I'm not the person choosing who moves up and who repeats. The only thing you can do is to help her when she asks, and keep her surrounded by positive energy. Half.... errrr, maybe three fourths of this sport is believing in yourself, trusting that your coach is always right, and working as hard as your dreams are big. Those three things do more to keep kids within the curve than anything else.