When my daughter was around the same age, she started expressing the same worries. My husband started taking her rock climbing, and being a part of that world changed her body image and helped her work through a lot of the control issues. It didn't change her perfectionism, but she was able to channel it into a sport where it meant she trained to compete on a national level until she started college. Climbing changed how she viewed her body; it became a tool she needed to take care of, so her eating was about health, not being a tiny waif. And she was proud of her muscles. And the kids on her team ate like horses because of the crazy amounts of calories they burned, so she learned to look at food as fuel so that she could climb longer and better. She avoided sugar, refused to drink carbonated beverages, but loaded up on healthy carbs and proteins - thanks to a coach to taught them about nutrition. And climbing let her be in control of her own success while it also forced her to allow some control to be in the hands of whomever was at the other end of the rope, so it really helped her with her control issues.
From my own experience, I would highly recommend a sport that doesn't focus on body image and that isn't totally a "team" sport like soccer or basketball. Swimming, running, etc. all allow for individual control over one's performance within the context of considering and working with teammates.
