At a certain point in 2006, I kept drawing these things I called "velveteen beanies". This is because they reminded me of a cartoon of the Velveteen Rabbit that had shaped the rabbit like this - a sort of "bag" animal, maybe like a woobie.
So here are the best ones. Just bunnysona, puppy, Dib from Invader ZIM as a cat, and a dogsona.