I really think boosting the amount of exp gained from low level quests and even from killing mobs (except for elite mobs, like in dungeons) would solve this problem. It would take away the extremely clear advantage that dungeon spamming has over questing. I am truly interested in exploring the new zones and quests and seeing how they've changed, but once I hit 15 and can do dungeons, what advantage is there to me to quest? Dungeons give significantly more exp, it's not a small difference at all.
As a quick example, I got the quest to go to Barrens from Durotar on my Warlock at about level 12. On my way, I dotted all the mobs and had my pet kill them and was pretty much 13 by the time i got to Crossroads. In two levels of straight questing, I'm already at the required level for dungeons and can pretty much just sit in Org while the queues pop. The queues are quick enough that I don't even have enough time in between dungeons to get a quest or two done.
As a side note, Azshara was redone and hugely mentioned as a low level questing zone, but how would any new player know to go there? There are absolutely no lead-in quests nearby, there is only the one to go to Northern Barrens.
EDIT: Perhaps a free flight from some NPC in Durotar to get to Azshara would help.
But even to new players, why would they ever bother with questing when the fastest way to get to 90 is through spamming dungeons? My big question is, What was the point of redoing 2 massive continents' quests just to have a simple spam of dungeons be the fastest way to 90? In Outlands and Northrend, I didn't even make it out of the starting zone before I was 68 and 78 and moving onto the next expansion.
I guess another topic that comes to mind is that it's sad that once an expansion is over, it's over. It's dead content that a huge portion of players will ignore: all the work that goes into the landscapes, NPCs, quests, creatures just drops in relevance by an unbelievable amount. Bringing back questing would at least bring back some of this wonderful content. I honestly love both Outlands and Northrend. And it's also a little weird how Blizzard hasn't learned its lesson yet. In maybe 8 or 10 months, Pandaria is going to be a wasteland just like Northrend and Outland are (and the rest of Kalimdor and Eastern Kingdoms, for that matter).