How wonderful you are, to open your home, to a child in need, and with struggles, no less.
I was always interested in doing that too. If you care to share your personal experience, plz msg me, and let me know how time intensive it is, and also, how much impact it has had on your other children, if you have any.
Anyway, I have an idea. What about maybe pottery? You can perhaps find a studio, or they have those little pottery cafes, or buy the clay at an art store. She would be creating something with her hands. She may really enjoy it.
Perhaps dance or gymnastics classes. Phsysical activity stimulates the good endorphins and may help her "feel better" mentally while she is doing something fun.
If cost is an issue, and you feel comfortable while not jeopardizing her confidence or personal growth, perhaps inform the places you are interested in attending of her situation and maybe they will give you a discount, if they have the authority.
I also, totally and completely agree with the ideas of getting involved with animals to help her. There are so many things to do...and maybe you could even "foster" a cat or dog from a rescue group. If you need help finding a rescue group, let me know as I know a few!
All the best.