What exactly do you mean by a moral society? How does living in a moral society differ from living in a society where the individuals have a behaviour from the start that you would see as moral? We have been living in societies a long time, apes live in societies, so the behaviour would be older than that. I made a quick wiki search and didn't find any species in the evolution of humans back to when apes and monkeys start to distinguish themselves that didn't live together. Also, this behaviour would need some time to develop, but it seems to be fairly well developed in all apes. After all, that one instinct is less complex than everything else that distinguish apes from their next super-group "mammals" and even many of them show this behaviour.
To some extent. I can't account for exactly where beneficial instincts end and morals begin, but that's probably because there is no such line. Who are you to say that morals aren't instincts and socially learned behaviour? And who are you to say that the instincts that animals adhere to aren't etched into their brains in the same way as our morals?