I made some heavier kennel pads for my dogs on my old Singer 15-91.
I used white polyester gabardine and two layers of white fleece inside. This might not seem to make much sense, but the fabrics were tough, cheap and most important - they're bleach-able - I could run them through the sanitize cycle on my washing machine and they have stood up to many, many laundry cycles. The white fabric makes it easy to find stains for pre-treating. More practical than it sounds.
The fleece might be a better option than cotton batting, even if you want to pretty up the outside. I think you can get remnants of fleece at the fabric store to see if you like it.