Organic carpet?

One of the first things to do once we take posession of our new home on Friday is get some carpet (runner) installed on the stairs. If you've ever seen a bulldog go down stairs, you would understand why. Betty's center of gravity is in her neck so basically, in order to go downstairs, she falls and catches herself with each step. It is not graceful. In addition to wanting to assist her, leaving the stairs wood means that she could scratch them up in a matter of weeks. My point of all of this is that if I'm going to be painting with organic paints it seems silly to bring in toxic padding and carpeting. Is there an organic carpet company that does installations? I've considered sisal but am told that it can be slippery so it isn't advisable for stairs. Anyone have any thoughts on this?