If you define "soul" as knowledge of right from wrong . . . then the obvious question is: do animals know right from wrong? If your answer is no, then your other answer to the question of whether animals have souls is obviously "no" as well.
But if you could ask your dog what their definition of the soul would be, I imagine they might answer something like "the soul is the ability to feel pain, fear, hope, anger, love, hunger, satisfaction, happiness, excitement, comfort and discomfort, friendship, play, enemies, etc" I suspect an infant or even a young child would be more inclined to agree with your dogs definition than with the more exalted one of "knowledge of right from wrong".
Knowledge of right from wrong is a more advanced form of consciousness than what dogs and cats and young children have access to. But there are also forms of consciousness that many human beings have access to that are more advanced than the relatively simple one of knowing right from wrong. Such an individual might have a very different definition of "soul". So soul is a relative term depending on an individual's level of consciousness, and there is no reason one defintion should hold a monopoly over the others, except for that those individuals "think" it ought to.