Mauser,
The problem with carpet is that it doesn't heal much at all. If you hit the same spot more than a couple times you'll then have a hole. If you do use hanging carpet, use two or three layers and just check it now and then.

Used carpeting can usually be obtained at carpet retailers that do installations. Very often they bring back carpet they have removed and throw it in their dumpster. My first car had the plushest interior you ever saw

The other problem you have is with a fenced area, you prolly won't be able to see what's going on on the other side. Just be really really careful okay?