Level with a pet if you can because it will help keep you safe. If your pet is tanking all of the damage from the enemies you’re fighting, you won’t have to. The other reason is that pets are easier and cheaper to heal than you are. If you don’t have a pet, make sure you know how to use your defensive abilities. You can’t level quickly if you are dying all the time.
Island expeditions - Set sail for the previously unmapped isles of Azeroth. Battle in groups of three as you race against cunning rival intruders—or enemy players—to collect the island's resources. Constantly evolving challenges await as you traverse frozen landscapes near Northrend, open the gates of an abandoned Gilnean castle, navigate a war between elementals and more. Can be done either in PvP or PvE against advanced AIs.
For reference, my previous best time abusing Method-0 in 7.3.5 was 32.4 hours(as show in the old thread). A difference of just over 8 hours; which isn't all that bad, all things considered. And I believe I made several errors along the way, which could be cleaned up in future runs. I believe that that gap could be significantly closed by using a monk's bonus, but I hate playing monk...so...yeah. YMMV
Island expeditions require groups of three players to venture to islands with randomly spawned enemies and piles of AP. The island expedition ends once they collect a certain amount of AP, and they are granted about 300 AP as a reward — unfortunately, players don’t get any of the between 6,000 and 12,000 AP they collect during the expedition. These missions can take anywhere from three to 20 minutes, and never once offer any real challenge or depth.

And, of course, there are plenty of in-game addons you can use to make your adventures in Azeroth even more efficient. Try checking out Azeroth Auto Pilot, which points you where to go, handles all your NPC discussions and quest turn-ins, and automatically sells your junk gear (among other features). Deadly Boss Mods is still a must-have, so you don’t die in dungeons quite so quickly. Pawn helps you tell whether the gear you’re getting is actually an upgrade or not. World Quests List gives you a much better way to see what’s happening in your zone (and sort for the rewards you’re prioritizing).
I do not recommend going for TBC, although I remember Hellfire peninsula to be decent, everything else is rather slow. Instead go for WotLK, Borean Thundra gets you levelled very fast, and then you can head straight for Icecrown at 67, which is also insanely fast, although admittedly has a few elite quests. You can go to Sholazar Basin alternatively. 2 zones should get you 60-80 no problem.