What type of hard flooring can I put over carpet?

I have a new house with new carpet and I have designated one of the rooms as the "pet room." This is where the rabbit, chinchilla, and atiel reside. I am trying to figure out what I can put down over the carpet (which is a shag carpet) to protect it: I'd like something water-resistant and non-toxic that can't be chewed or dug up, and that would be easy to sweep. I've looked at interlocking floors, but I don't think any of them are supposed to go over carpet. The best idea I have so far is to custom order a large chair mat. Any other ideas?