tl;dr- Quantum computers can't really help us to simulate the whole universe as the universe is likely vastly more complex than even quantum mechanics can capture, plus we can't even begin to guess how big it is or many other basic fundamental features. In short, simulating the whole universe is beyond sci-fi.
We can't really simulate the entire universe, in large part because we have no idea what the universe is.
I mean, at current, we have a vague picture of the observable universe:
And we've got the Standard Model that describes our current best guess at describing much of what we can see. But, beyond that, we don't know much.
Examples of stuff we don't know:
Is the observable universe a significant part of the larger universe? Or is it unimaginably small compared to the whole?
Is there a lot of weakly-interacting stuff out there, e.g. dark matter, that might compose what'd kinda be like a parallel world?
Suppose dark matter is real (which many physicists currently believe). Then, what if something weakly interacts with dark matter, but only with normal matter indirectly through affecting dark matter? And what if that's a recursive relationship - do we even know a non-trivial portion of what exists within the domain of the observable universe?
What exists at the bottom? We really don't know much beneath the Planck scale; it could be the case that what seem to be fundamental particles to us are actually unimaginably large universes themselves!
Extra-dimensions, what's-in-black-holes, string theory, etc., etc..
Basically, we know essentially nothing about the larger universe other than that we're part of it. Given this unimaginable ignorance, merely having quantum computers won't really help us simulate the whole thing.
That said, what quantum computers can do is help us simulate quantum systems of comparable size as well as a bunch of other interesting problems. Presumably we'll gain a better understanding of the possibilities as time goes on.