How can I get a mate with a full grown pup?

If it is the only animal in this family tree then you only need to be level 10. However, if you have 2 older animals you'll need to get the pup to level 50 (or pay with gems) to unlock a new family tree where you can transfer the pup over and start a new family, you can still play as the other animals on the other family tree, you just need to change the family you play as in the main menu in the tree icon in the top left corner of the screen. 😃