What's the gym's philosophy? I know of some gyms who want the kids to work at a certain level, and aren't really bothered what the individual wants. There was a really talented child in DD's group they kept moving into the elite group- they all train at the same time, so it was just a matter of putting her with the older kids or a different group.
Every time they did she would quit. It took the fun out for her. There'd be discussion and agreement to let her go back to the old group, and it'd be OK for a while, then she'd be doing the conditioning with the elites again, then certain skills, then it got hard and she'd quit again. There's been quite a few kids found the 15/20 hours a week hard, and they let them quit rather than adjust the hours. DD quit as she wanted to do 12 hours per week for the summer rather than 15, and they wouldn't allow it. These were (old) US level 4/5/6 sort of standard.
Where DD is at at the minute they do what the kid wants. They work on the principle that if a talented child is unhappy, they'd rather back off them for a few months and keep them training than have them quit. So there is always the option to move down, sideways, to a group with friends, to train less, or more. They're a much bigger club though so there's more options.
I think presenting the idea to her as "try it for 3 months" is a good one, if the club are OK with it. Then she knows if she's really unhappy she can go back to her comfort zone, bit of a safety harness for the leap into the unknown