Your child can create a whimsical paper pet Dr. Seuss would be proud of.
Fold a piece of card stock in half. Draw an animal onto the paper so that some part of the top of it (head and tail, or back) is along the fold. Cut through both layers of paper, being careful to keep some of the fold intact. Attach the googly eyes using glue if they don't have adhesive backing. Now stand the animal up. If it splays apart, glue together the front and back of the head and tail, leaving the legs unglued (or in the case of an octopus, glue just the left and right arms and leave the bottom ones unglued).