I don' t know exactly how the word "DQN" became so popular, but I think this word sounds so fun because it (=dokyun) reminds many Japanese of the sound of a gun. It is easy to read, write and pronounce for the Japanese 2ch'er.
And I want to point out the fact that "DQN" can be changed into other expression. (in Katakana, ドキュン (dokyun) or ドキュソ(dokyuso))
2ch'er tends to change the word or phrase just like the example >>6 san provided us, and we are always looking for new words or phrases.

If my response can't help you, スマソ(=スマン or I'm sorry)