Quirrell will be killed by Harry at the end -- but this is all a part of the plan.

Suppose that Quirrell is not the original Riddle, but is just another Riddle's copy. If Quirrell and Harry are both copies of the original Riddle, the original Riddle had no reason to prefer Quirrell's life to Harry's life.

The story about a good hero saving the world by defeating a horrible villain: he did not have to fake it. He could make it real, by letting two of his own copies fight against each other. Realistic hero Harry will be better than a fake hero; he will be more authentic; there will be no risk of discovering his secret in the future.

Just like Harry had a magically induced blind spot in his mind, also Quirrell can be manipulated. (Memory changes, imperius, unbreakable oath... there are many options.) This is why Quirrell does not kill Harry, why he teaches him things, any why he is making him angry at the end. This all is Quirrell's purpose; he is just a tool to prepare Harry for the role of king of the world. Quirrell is not optimizing for Quirrell; he is optimizing for Riddle.

So, this is what I imagine: First Riddle created his copy, Quirrell. Maybe with a specific purpose, maybe just as a backup copy. But later he was not satisfied with the outcome, when he realized that his new memories will not be preserved. So he later created another copy, Harry, killing himself in the process. Before that, he somehow magically commanded Quirrell to train Harry for the role of the king.

Quirrell may not be aware of this, because he was magically brainwashed. This is the power he knows not, the power that will cost him his life at the end. He is actually magically forbidden from killing Harry.

Not sure if the original Riddle was a sociopath (that would explain why he doesn't mind his two copies fighting to death against each other), or whether Quirrell's personality is another effect of the magic, preparing him to be the perfect villain.

Anyway, when Harry outsmarts and kills Quirrell at the end... this is exactly what Riddle has planned from the beginning. This was his plan for becoming a hero. (Maybe there will be a moment when the victorious Harry/Riddle will regain all original Riddle's memories. Or maybe not, because that could make him behave less authentically afterwards. Or maybe yes, because discovering that your favorite teacher was actually Lord Voldemort and defeating him is the most appropriate moment for a minor personality change.)

EDIT: Oh, now it's obvious what is in the mirror, any why Harry has to be there. The mirror contains Riddle's memories that are to be implanted in Harry soon. By the way, Dumbledore already knows many of these things, and has his own plans.