After reading comments in /r/hpmor, I've realized that Professor Quirrell has a superior move in the previous chapter, which has hopefully updated or will update soon.

Be honest, Eliezer; you just got sick of all the naked Harry jokes.

How I laughed when I realised it! When I saw you had made a Good Voldemort to oppose the evil one - ah, how I laughed!

I guess now we know what Dumbledore was laughing about in chapter 17.

The Cloak of Invisibility was torn away from him, and the shimmering black Cloak flew away from him, through the air.

Professor Quirrell caught it, and swiftly drew it over himself; in less than a second he had pulled down the Cloak's hood over his head, and disappeared.

Quirrell can escape the trap because he is no longer reflected in the mirror, being hidden by the True Cloak of Invisibility. All he has to do is walk out of the reflection, which he did.

Into the hand of the Albus Dumbledore flew from his sleeve his long, dark-grey wand, and in his other hand, as though from nowhere, appeared a short rod of dark stone.

Albus Dumbledore threw these both violently aside, just as the building sense of power rose to an unbearable peak, and then disappeared.

The Mirror returned to showing the ordinary reflection of a gold-lit room of white stone, without any trace of where Albus Dumbledore had been.

After reading Reddit, my interpretation of this scene is that Dumbledore realized Quirrellmort would not be affected by the trap, and that the only result would be that Harry would be trapped eternally outside of Time. Dumbledore makes a split-second decision to sacrifice himself in order to save the boy, throws the Elder Wand and the Line of Merlin Unbroken out of the mirror's reflection so that they will not be trapped with the headmaster, and trades places with Harry just before the Process of the Timeless (the rising sense of power) finishes. Albus Dumbledore is now trapped inside the mirror forever, and Harry Potter is back in the real room with Professor Quirrell.