Oh please. There are certain things that are universally immoral, including rape, child molestation, elder abuse, abuse of the disabled, etc.
Even if that is the case, that still doesn't make morality immutable and universal, which is what you said:
Morality doesn't change with the passage of time. Or least it shouldn't.
You are, essentially, saying "This is universally immoral. Therefore, morality is universal and immutable." This is a logical fallacy known as an "
irrelevant conclusion."
You are also making two
very big assumptions: The first is that these acts are universally considered immoral; in many cultures today, rape isn't seen as immoral, since women are seen as sexual toys. The second assumption, on top of the first, is that they
always have been and that just isn't the case. For example, many cultures disposed of mentally or physically disabled infants.
You can argue that those acts are wrong today and were wrong millenia ago, it's just that humanity wasn't as morally evolved then. But that makes my point all the more salient: morality is a set of codes undergoing constant change. I can certainly agree that a kind of "ideal" universal morality might be possible in the sense that once you take
everything the answer depends on and consider it a part of the question, the answer is necessarily inherent in the question.
In other words
if you could somehow include
everything that morality can depend on, perhaps you could define an "ideal" universal and immutable morality. But can you do that? It's a very big if.