You sir or madam are playing this game for the wrong reasons.

If you don't care about the story, just go back to WoW already. This is a story-based game. You are not supposed to just rush through it to get to the expansion. All you will be doing in the expansion is continuing the same story after all, and if you've been skipping it until now, you won't care about it then either.

The leveling and ilvl thing was also nerfed massively when the expansion came out, so you don't have to do any grinding whatsoever. You gain a ton more exp and get all the gear you need just from playing the story now. I have no idea how you've managed to not be high enough ilvl to do a dungeon, since I never had that problem and I did it BEFORE you started getting free gear. You NEVER have to craft or buy gear in this game. Trust me, because I never have.

You've probably not been paying attention and missed out on the gear you should have gotten. Like not doing your Job quests, or not using your Tomestones of Poetics to get easy ilvl 120 gear.