The absolute fastest way outside of professions is to make sure you hit level 80 while still having a good number of high level zones not done. Quests at 80 don't give experience, so they'll give you a fair chunk of gold instead.
To make sure you can do this, make sure you don't go to northrend until you're level 70-71 (even though you can start as early as 68. It makes quests easier if nothing else, and there's that gold waiting at level 80). Make sure you do all/most of the quests in a zone (ie, get the achievement).
Also make sure you do at least one daily pug each day. Besides the experience coming from a non-questing source and the gold/experience for pugging, you'll start earning emblems of triumph for your level 80 gear. Of course, you only get them on your first pug, so you really don't need to do it more than once a day.
Doing all that, it's pretty easy to hit 80 while you're in Grizzly Hills or Zul'drak at the latest. That leaves Sholozar, Storm Peaks and Icecrown to do gold quests in.
The one bad thing is that the good dailies require some pre-questing in those three areas, so you won't immediately have access to some of the good daily quests at once. That said, it's still worth it to save those areas for last, with a few exceptions.
Because of time restrictions, you'll probably want to get an early start on the Sons of Hodir chain if you don't have any other level 80 exalted with them (due to the shoulder enchant being BoA), and the tournament chain takes one week to unlock the majority of the dailies, and there'll still be more that won't unlock until you're exalted with -every- horde (or alliance) faction as well as argent crusade as well as the sunreavers. That takes a while, so getting started on all that early is a good idea (I think you can from level 77).
All the other dailies can be unlocked as soon as you finish the pre-quests though, so it's entirely possible to have them all unlocked in one day (if you are the dedicated/insane).