Main story quests usually aren't that bad, as they drop ponies and other shit that even max geared raid players sort of chase after. That, and farming the "lights" for one of the relic stages goes faster if you do non-endgame 8mans. But yeah, being DPS is going to suck and the only thing that will really make it unsuck is to make friends with a healer or tank. Or a healer and a tank, and then your life is cake.
WoD is 120 ilvl, and you should definitely get your story to that and past so that you can unlock the weekly, which will let you get an ilvl 130 weapon in a couple of weeks. It isn't main story quest and it really just involves clearing labyrinth/st/wod once each to unlock, then you just do all 3 again each week for the quest. The queue time for those, especially the first couple of days after a reset, are quick even for dps comparatively.