In 1996-1997 I received a toy set for Christmas. I barely remember it but I know it came with three animal “families”: bunnies, cats and dogs. I don’t have all of them anymore, but I know the biggest animal’s head pops off. The rabbits are white with red eyes, the one dog I have (medium size) is a border collie type standing sideways and the largest cat was white and in downward dog position.
I’ve been scouring google for three days and although it’s similar, I don’t think it’s the littlest pet shop.