I took both my sons down to Moab for spring break one year when they were in their early teens and rented a jeep. They still talk about it fondly to this day, over a decade ago. We has a ton of fun with them driving through streams, up and down 4-wheeler trails and back roads. I did all the technical driving on the trails and took that poor jeep many places where it shouldn't have gone. Wish I had a video...
I agree, get her on a go-kart track! It will only help her driving skills and be great fun too.