H.S.
We are going through something similar with our son (10), and have seen a nutritionist, specialized in children. That was helpful - maybe something you can try.
The goal for kids like my son, who is 95% in weight and 98% in height is not to loose weight, but to slow down the gaining of weight. Instead of gaining 10 pounds over the next year, we are trying to limit this to maybe 3 or 5.
From what I learned, just walking on the treadmill will not make her loose weight, and I would be worried that she would totally give up if she sees nothing is happening. But exercise in general is so important, and she should keep at walking for other health benefits!
We did get a small indoor trampoline, and it gets some good use. We set it up in the family room, and often he jumps while I am making dinner.
Food intake is a big factor and I think you should give her all the support she needs, but as you said, to support a healthier way of living and not to loose weight.
You should let her have good meals: good breakfast with protein, a small snack to carry over to lunch (fruit or veggies would be great), a lunch (check your school lunch menu, often they are not the healthiest), then a solid afternoon snack with protein (jogurt, nuts, some crackers with cheese, veggies, grapes and cheese) and dinner. The reason to have snacks is that it helps your body not to crave food for the main meals, and then overeat. The nutritionist also recommended a large glass of water before dinner (or before a second helping) and eating slowly. And don't make her finish her food before having dessert.
If you are concerned about what she physically can do with her CP, you should consult your kid's doctor. A lot of YMCAs and other kids gym clubs are offering programs for kids, and this also could open her eyes to a wider variety of body shapes.