I got a "cpu caddy" from amazon, I've got an all carpet floor too, and so far it's done a good job of keeping dust out of the case. We also vacuum the floor about twice a month, doing that would probably help the most.
Popular alternatives to
Allsop Metal Art CPU Caddy,...
VIVO Computer Tower Desktop ATX-Case, CPU Steel Rolling Stand, Adjustable Mobile Cart Holder with Locking Caster Wheels, Black, CART-PC01