Kipper switched gyms at 9. At first, I talked to her about possibly changing and it was clear she was TOTALLY stressed out about making the decision. Ultimately, I told her that I was making the decision to leave the current gym. However, she could decide which new gym to attend. She was instantly relieved since I took the "big" choice off of her. She tried out a couple of gyms (I picked for her to try) and chose the toughest, most focused of the two. The change was hard bc she was close to former team mates. However, within a couple of weeks she had built bonds with her new team. Don't underestimate the pressure it will put on your dd if you "leave the choice to her". So, if you KNOW it's time to move, then DO IT!
On another note, I met a new parent in our gym's lobby who moved her 7yo dd from another good gym in the area because our team won more, and "if the tuition is the same, she would rather win". I don't think winning at L3 is a really good measuring stick to use. But there are LOTS of other good reasons to choose or leave a gym.