Qarn is all about your DPS. This dungeon is pretty much all them from the first boss to the last.

Bees need to be burned fast. You can take your good sweet time on the boss himself as long as you're dropping the bees before they hit with Final Sting.

Golem's heart needs to be broken as quickly as possible to avoid him dashing all over the place and wrecking everyone. It threw me for a loop when he took off despite having full aggro on both Golem and Stone. But again it's primarily the DPS who have to make sure they take out the stone fast and then pound him down once he's stunned.

Last boss is again all DPS because in truth the boss himself can be solo'd by the tank even without a healer (talking as a WAR on that one). The verges and the heads drop fast once a DPS is on them and then everyone can go back to the boss.

So ultimately Qarn is a challenge to the DPS classes. It's a wake-up call that just hitting three buttons while focusing on one mob isn't going to be enough going forward. The tunnel-vision comment above is spot on.

As for the best group I've found with this dungeon I've found the best DPS for it to be the Bards. Ranged DPS means they can keep pounding on the high priority targets while handling the encounter mechanics.