I have definitely heard venison is good for allergies. One girl was actually surprised that her dog was allergic to it and stated that of course her dog is like the ONLY dog allergic to venison. I would definitely try it. Delta does very well on venison. Lamb is also a good thing to try if you can, although I know in the U.S. it's pretty expensive.

Rabbit might have not given Digi a problem because, even though it is a 'red meat', it is VERY lean, so most consider it something like a white meat chicken almost. I am jealous. Lol I want a rabbit. My friend has one she's been meaning to give me.