I am looking for a toy from the 1960's my mom used to have. We think they were called "Moon Doggies"

But we are not sure. They shaped like a rectangle, about 8-10 inches long and 3-4 inches wide. The under part was made of suede and fur, and the top would have fur that was dyed different colors. And when you would pet it it would sort of wiggle up-words like a wave. My mom said that they used to pin them to thier shoulders. Does anyone remember them? Or what they were called?