Be careful, once she starts showing one animal she will want to show more.
We used cat carriers or small dog cages for pairs with towels in the bottom. Keep your eye on the local garage sales. As far as the illnesses go, that is something you will be taking a chance at unless your fair requires testing, which most don't. As far as the pecking order, unless the bird is on the top chances are it shouldn't make much difference. We never had a problem bringing any home. I think they were missed. Good luck to you and your DD