"The type carpet used if possible is 100% cotton felt. Most pulp paper making companies have lots of it and dump it at the dumps."

Don't think you will find any 100% cotton carpet, most carpet these days is synthetic or nylon blends. I'd stay away from berber or loop pile, as they will snag on the dogs nails and cause a runner in the carpet and potential injury to the dog. You can go to a local flooring store and catch an installer, for a few bucks I'd be willing to bet he will pull a whole room(s) of decent carpet out and get it to you. I'd go with a cheap plush or cut pile berber.

As far as padding goes, stick with something low, like a felt or rubber pad. The rubber padding can be found in older homes or nice hotels and is hard to wear out! A multi purpose glue found at a local box store will secure the glue for the padding down on the plywood with a small notched trowel, and repeat with the carpet over top of the pad and I'd also staple the edges underneath of course. Good luck!

S_B