Well, there’s no mention of Spot or Kitty in the Gospels, so it’s hard to say for certain. I’m guessing that pet ownership was not a big thing in Nazareth during Jesus’ lifetime; most families would probably have only been able to afford to keep animals that were useful in some way (food production, etc.). It’s fair to say that Mary wanted Jesus to have an enjoyable childhood and to learn (as all kids must) about responsibility, but having a pet was probably not the way that those things happened.