You can try the peroxide and sun method. The sun won't further burn her because the UV rays won't be able to act on the plastic. Putting the peroxide in the sun simply increases the change of the peroxide to water and oxygen (that's why it's sold in a dark bottle and not a clear one) The whitening action is due to oxygenation, not bleaching (which is what putting her directly in the sun does). It isn't the UV acting upon the plastic, but the sun acting upon the peroxide that works. It acts pretty quickly, so do it on a sunny day when you're home all day so you can go out and check her often.
EDIT - The peroxide turns into water and WILL intensify the rays of the sun if left out, plus the extra oxygen created will have dispersed, so the oxygenating action will be exactly the same as regular tap water...so pretty much nothing. The conversion of peroxide into water and oxygen will only take a few hours.