Is morality built into our cells?

I just read a question where somebody claimed it was moral to not kill mice because he or she felt a warm, fuzzy feeling inside when looking at the mouse as it was being drowned. It reminded me that I once read somewhere that babies have wide eyes because we have a built-in feeling that makes us want to protect babies when we see those eyes.

I would argue that there is a cuteness “factor” built into us, and I think it makes us want to care for things we find cute.

So here’s my proposition (and it’s probably not just mine, but I can’t quote anyone right now, so I’ll take responsibility). I think that cuteness comes first. It is an evolutionary thing that evolved because it helps us survive as a species. Before we ever had religion or any morality, we were still treating babies like they should be protected. Good thing, too. We wouldn’t be around if we didn’t.

Morality came later, I postulate. Morality is the application of reason to naturally occurring behaviors. It’s a justification or explanation for why we do things. However, since it’s a naturally occurring behavior, it doesn’t follow reason perfectly. Love for human babies spills over to love for cute mice.

Then, since love for babies is supposed to be moral, we mistakenly spill that over and some people say love for mice is moral.

Is that the way it is? Or is there something I’m missing? Where do you think morality comes from?