If she's that into it, but isn't ready to be in a group, then maybe it would be worth the splurge for some 1:1 coaching time. All our local gymnastics places offer that as an option. The nice thing about it is that you could focus on the moves she does, to make sure she does them well, or maybe fill in some gaps of intermediate steps to make sure she doesn't hurt herself. It could also acclimate her to the gym environment (with classes going on around her) that might help as an intermediate step to group classes, too.
It is very important for her to learn the proper forms, even though she seems like a natural. (Tucking her head into a roll?!?)