Quick thoughts: yes, it would fire. As Tommy Lee Jones reminds us, pistols (not just Glocks) can fire underwater, if you’re stupid enough to do so (like you’re performing DIY Shock wave lithotripsy) — they carry their own oxidant.
The bullet would travel faster, too. There would be less drag on the bullet, so it would not slow down as much as it does at one atmosphere. The muzzle velocity would only be epsilon faster, but the overall speed at some arbitrary distance would be higher.
I don’t understand why Danae doesn’t find that interesting.
(Blam! and Ping! not really happening, of course, in that rarefied atmosphere)
Update: the speed to orbit near the surface of the moon is about 1680 m/s. Not achievable with a pistol, but within the capabilities of some advanced weaponry. Escape speed (1.41 times higher) would require a Bull-like supergun.