Dog and allergy friendly floor coverings?

I have hardwood. I have dust allergies. I have a dog.

So I need something to cover my hardwood and protect it from the dog, that won’t collect dust and make me sneeze. I love the smooth floor because it’s so easy to keep clean, but the dog’s nails are scratching it. What’s a good, inexpensive kind of mat that isn’t like a conventional rug or carpet?

(Sorry if this is a misplaced GQ …)

Have you considered sisal rugs?