I've been where you are...because I quilt others think I have nothing more to do than help them 'repair' a quilt. Sigh. What I would do in your place, is refill that hole with pieces of batting that can take the heat (what pot holders are filled with), then I'd use small scraps of material and hand patch the holes to as close to the original fabric as I can get. Remember, those places where the burn marks are, will burn again eventually in the same spot due to her falling asleep.