It could very well be that any individual species could come up with a unique and novel trait that no other shares, but that in itself would not be proof of divine. But I'll grant this concession for the sake of argument and say that if morality is a novel trait amongst humans it will give weight to the claims of morality being god-given. So with that I present a challenge for all men (or women) of faith to demonstrate this notion:
Find a bear who has recently given birth to cubs. Then proceed to attack the cubs in front of its parent.
Unlike us, bears have no higher moral base. They have no ability to rationalise whether something is right or wrong, yet I would be willing to bet that a bear mother would protect it's cubs to the death if need be. Living in Australia, I see a very similar behaviour from some of the birds - and every spring this means that I have to be wary of magpies swooping me in order to keep it's nest safe.
Neither a bear or a magpie has to rationalise this behaviour, it's wired in their brain and in their genetic code in order to behave this way. Just as with the male emperor penguin that will in winter spend months standing still in order to keep the egg warm, then trek for 40 kilometers to get food to feed to it's offspring. The protection of the young is hard-wired into animals because as we understand life is that it's an immortal journey of the genes contained within. Life is geared towards survival, so our mortal coil is prolonged by investment in future generations.
From that, it should follow that protection of the young is hard-wired in us too. That we don't need a higher power to tell us to protect our children, but that 3.7 billion years of evolution has meant that survival strategies that give help to the future of our species, and especially the future of our genes, will form the basis of any desire to protect children. I would argue that in the absence of any particular doctrine of behavioural conduct, we should still see parents protecting their children because quite simply we are wired to do that. The survival of our species depends on that very notion, and humanity survived for just that reason over the course of the hundreds of thousands of years before the invention of religion to mandate behaviour.