Which morals are universal across the species? This is the first of a series of three questions about morality:  

There are sets of moral standards within any given society. What one society deems as acceptable may be deemed as abhorrent in another. This concept lends itself to the idea that some aspects of morality are learnt and not innate within an individual.

Which morals are universal across the species?

The second question: What is the psychology of morality?

The third question: How is individual morality linked to psychological profiling?
This is a partial answer to your question.

According to "Only Humans Have Morality, Not Animals", (Guldberg, 2011), claims that morality is something unique to humans.  Basically the author concludes with:


  Human beings are not perfect and never will be, but we are special and unique among the animal kingdom. We are capable of making judgements about our own and other people's behaviour, and have the capacity consciously to change the way we behave and society as whole.


A key argument made in the article is that there is a great difference between instinctual connections and actions and human empathy and morality.

Further, according to the article "Is Morality Innate?" (Prinz), proposes that:


  Morality is a byproduct—accidental or invented—of faculties that evolved for other
  purposes.


and proposes a somewhat negative, yet true conclusion:


  Nonhuman animals are often
  violent, but their potential for bad behavior may be lower than ours. Because we can
  reason, there is a great risk that human beings will recognize countless opportunities to
  take advantage of our fellows.


Essentially, it seems that perhaps morality is unique to humans owing to our abilities to reflect, reason as well as react.