I think I'd put some other light material over the tyvek, to make it comfy, warm, and to keep claws from tearing up the tyvek. Does your dog have a favorite blanket? (You could make a cover out of that, and not take the whole thing).
What I am making is a peiece of tyvek 2 1/2 foot my 3 ft. Another peice of vellux blanket the same size. I will set them together and leve one short end unsewn. This is how I will slide in the z-rest when he is on the gound. So I can remove the pad and have that blanket/tyvek for in the hammock. The vellux is pretty durable, but stretches a lot. I've got some 1.9 I can throw together for a quick dog hammock to see if he likes it just for a test.