Personally, I would not move in given these circumstances. You can't really demand that she give up her pet and she can't demand that you suddenly become unallergic. There's a sort of fundamental incompatibility.

Having you sleep on the couch instead of the dog sounds insulting to me. The only way I could understand that one is if it has to do with the twin bed and not the dog -- two people in a twin can be impossible. Are you going to have a bigger bed when you move in together?

I am not sure if you have lived with a significant other before -- if you haven't, it's a lot of work and A LOT of compromise, sometimes so much compromise that living alone seems preferable.

I would try to have a conversation with her about how you will handle these kinds of differences when they come up, just generally.