I would use a cotton backing. I'd be nervous that the front and back of the quilt would shrink/wear unevenly if I used a cotton and a synthetic on the same quilt.
Little kids are really hard on quilts and that's how I like it. I always tell people, "Make sure you use this quilt. If I can't find a stain or a rip on it, my feelings will be hurt." That fixes the nervous nellies every time.