Having been the owner many bunnies, I would be afraid they would chew whatever mat they had. Personally, I would rather mine eat a natural cotton item than something made with micro fibers. As fill filling, I would suggest a light layer of snips, strips and leftovers layered between whatever top and bottom you decide to use. Sewn together as you suggested and sewn the lines to to keep the filling in place. Perhaps an old T shirt in place of the outer fabric? This is what I used to line baby bunny baskets when I doing wildlife rehab work. Just my thoughts.