What exercises should a 12 year old gymnast do?
How much time is she already training? Are you training her specifically to improve gymnastics performance? What level gymnast is she now?
I am going to assume she is doing a fair amount of tumbling now. So I would avoid anything with a plyometric type of element. I am very big on athletes doing water exercise, deep water and shallow water. Shallow water might be difficult to arrange for a 12 year old female gymnast if she is not tall enough to stand on the pool bottom with her shoulders out of the water (at least her shoulders out of the water). There are a lot of great core exercises that can be done in both water depths.
I would also advise you to be careful of her training volume. If she is training competitively, you want to be aware of the symptoms of overtraining. And I can’t remember where young gymnasts are in relation to their off season and competition cycle right now. The status of her current schedule is important.
If you want to give me a little more information. And do some back and forth conversation. I would be happy to discuss this at length. Just respond to this comment or contact me through my profile. There is so much I would want to know in order to answer this question properly. Like injury status and history. Height, general body type and general weight (Is she low, normal, or high on the body fat scale. Avoid talking weight with gymnasts. Even though it is important for training design. It is also a delicate subject for young athletes.) Current exercise/workout volume and frequency. What type of conditioning is she doing at her gymnastics practices? Is she using any type of recovery strategies? Sleeping enough? Hydration? Pre and post workout nutrition/eating habits? Are you good at assessing weaknesses and imbalances in clients? I am just starting to phase athletes out of my work. But enjoy discussing all things exercise related.