J.L.
I would definitely seek a more informed pediatrician, but for a quick immediate fix you can do a couple of things, 1. put a tie down hat on her or
2. put some non-toxic yucky tasting something in her hair to help break her of the habit. (I don't mean to sound weird, but if I was as concerned as you sound I would rather her have pickle juice or something on her head for a few days, than to lose her hair).
The eating would be a major concern for me-have you googled this habit?