Identifying an Old Stuffed Animal?

I have a stuffed animal that I've had since I was a baby. And it was my mother's before me. It is a dog, that is what I was told, but I called it "Bunny". It use to be pink on the ears, arms, and legs. And it also has a music box. My mom is 37 years old. I'm not sure how long she's had it, but maybe that gives you an idea. The music box doesn't play anymore and I've always wanted to replace it, but have never been able to find the right melody.