Is it possible to post pics of any areas that she is losing hair? I am just about cluless when it comes to derm pics, but I think maybe some other YT'ers could take a look
Have you tried Atopica? This would be for envir allergies. If it works, then you pretty much have your answer. Not the healthiest drug in the world, but a very good choice. You could do the bloodwork. Personally I'd try the drug first. A bit backwards I suppose, but that's what I'd do.
It sounds like rabbit and potato were novel to her when you started the 12 week diet, so that really makes me think it's not food. But I don't have a list of all the ingredients in that food in front of me.
If antihistamines aren't doing much good after 2 or 3 weeks, I don't see a reason to keep giving them (unless they are helping slightly). You can try steroids and they may work, but that is really covering up the problem.