A simple way of understanding morality is pay attention to your interaction with your pets and vice versa. Do they try to eat you? attack you? Or do they see you as family and exhibit natural inclinations to cooperation with you? Do they expect you to mistreat them? No. Are they christian? muslim? atheist? No. It has nothing to do with religion, morality is natural. You don't need a book to tell you what you like or dislike. The concepts you form are then transferred to paper and the written word is a snapshot of the mind or moral values of those who wrote it. Simple.
The problem with morality is when its misunderstood as being outside of oneself or control. Morality should and can evolve just like any type of awareness. The development of empathy and other types of awareness is a product of this evolution.
Interaction with pets is not based on morality on their part. If you never feed them or take care of them, and beat them regularly, they are unlikely to look on you as a family member.
You can "teach" a pet right and wrong only in terms of what it can expect otherwise, but would you take the same chances with a wild dog you happened to come across?