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It is absurd, especially if you are dps. The queue takes no short than 45 minutes on my server, and even though I unchecked "in progress" I still get stuck in a fail group where everyone is in the process of quitting and I get stuck IN the dungeon by myself or with another person or two....who eventually leave as well because no healer or tank is coming in.
The quest says to specifically use duty finder, so I am not sure if just running the dungeon with a pug will work. Even then as dps trying to find a group manually is tough as well.
All in all this should be a side quest, I do not recall any MMO's where this type of thing was in the main quest.