If you raise a puppy found somewhere in the game (or the one that you bought), then its level will not change as a result. In order to increase the rank of your dogs, they need to be crossbred. Then the puppy obtained by crossbreeding, grows up and increases his level. Or… he does not. With some bad luck, the grown up dog may keep the same rank as its parents. If it happens, do not despair, some skills of your character and other dogs can increase the chances of success!