I know nothing about gymnastics. But in general, I guess my concern in moving a child up would be if she is needing to learn fundamental skills in the current class before moving up.

What I thought of when I read your post was how much DS wanted to play the violin when he started taking lessons at 5. But he needed to learn to care for his violin, how to hold it, and how to hold the bow before he could start playing. He did not want to learn those things--he wanted to play. But obviously, he needed to know those things before he could learn to play. If the gymn class is play based and is focused on exposure rather than skills then I can see that moving up might be OK, but if they are really working on fundamental skills, then it seems like a better idea to have her master the skills before moving her up.