I would stabilize the living daylights out of it. Maybe some kind of iron on, then stitch the square or whatever shape you want and then cut it out. That way the edge would be held together before it starts unraveling. Maybe fray check would be a good idea too.
But really..... maybe this wouldbe a good project for her to learn quilting and it'd mean so much more if she did it herself ;) (I'd be passing on this project)