You can find old suitcases online, at thrift stores and tag sales. If you want to keep the suitcase with its original finish, use a mixture of dish soap, white vinegar and hot water to clean the outside of the suitcase, removing any grime and build-up.
If you don't like the original finish, you can paint it like I've done here but be sure to use a binding primer first to assure that your top coat will adhere.
If you'd like the bed to sit up off the ground, you can add some feet.. upside down drapery viniasl and fence post tops to cabinet knobs and salvaged table legs will work. Once you decide, attach them to the bottom side of the suitcase. It's best to pre-drill some pilot holes first.
To keep your pet safe, remove the top of the suitcase completely or use two "l" brackets on the outside securing the top and preventing it from closing.
You can customize the inside with a new inspiring fabric or keep the vintage look. Now for the cushion.. grab a firm full pillow that will fit nicely into the suit case.
Add a protective pillow cover and a washable pillowcase or a quilted pillow sham to coordinate with the look. A sweet bed for your furry little friend. I'm Mrs. Fixit and t's just that simple!