A wooden cat is a toy that can be made using the Craftingskill, after partial completion of the questThe Great Brain Robbery. During the quest, 10 of them are needed to fool Rufus the meat trader into thinking they're real cats.
They can be made on the crafting table in your house with a regular wooden plank and one piece of fur (for example normal fur, bear fur or grey wolf fur) gaining you 15 Crafting experience. Attempting to use any fur from a Hunter creature will result in the message: "The only fur you have is too nice to waste on these cats. You should try something else."
When doing The Great Brain Robbery quest and it doesn't show up on the clockwork bench to make it, make sure you have progressed far enough in the quest.