It doesn't stand for anything. It represents the onomatopoeia "dokyun", which is the sound of a gun being fired. In the 90's there was a very popular TV show called Mokugeki Dokyun, which amongst other things helped reunite kids and parents who have been out of contact for a long time. And the people who were reunited (i.e. the ones who lost contact with their families in the first place) were overwhelmingly trashy people. Eventually it became a net slang to refer to trashy people as DQN.
It stands for Dragon Quest Nine. This was answered before.
"So, DQN stands for Do-kyu-m in Japanese, which means
A, someone foolish, mad, or out of their minds
B, someone with no or little knowledge on the topic other
2ch people are talking about.
C, someone who is a bit too childish to communicate with
others.etc.
Well, it's a little abusive expression, but
most of us think it deserves nuisances."
It represents our indomitable spirit, it stands for Don't Quit, Never.
Dorky Queer Nerds
It was originally based on Don Quixote Nigeria, which was an old Nigerian (obviously) fansite for the novel. Someone must have stumbled across it and thought it would be silly. Your "Mokugeki Dokyun" reason and the whole kyu-sounding-like-Q thing came much later.
Dank Quarter ounce of Nuggets