At level 80, I skipped Cataclysm and went straight to Pandaria. Even as my warrior leveled up, and that heirloom axe increased in iLvl along with me, Dugi still ranked that iLvl 87 sword higher. I kept picking up new 2h weapons, and Dugi kept rejecting them in favor of that Wrath sword. That's when I noticed that all of these Pandaria weapon drops, even weapons 20 iLvls higher than the Wrath sword, had secondaries under 20. So even though Dugi Gear Advisor is showing that a new weapon would provide a DPS increase, it still prompts me to re-equip that Wrath sword every time I equip a new weapon. Meanwhile, I've kept the heirloom axe in my bags, assuming that at some point its stats would once again beat whatever I had equipped, but nope, it doesn't, according to Dugi.
Also note that power leveling is sometimes used to refer to paying someone else to level your character to cap as fast as possible (i.e. they power level for you); a distinction used by Blizzard is to refer to the paid leveling as "power leveling service." This behavior is against Blizzard's Terms of Service. Power leveling yourself, which this article covers, is perfectly acceptable.
As late as possible. Early on, you’ll want to follow the missions in Battle for Azeroth right up until you get the option to send a follower on a two-hour long quest. As soon as you get there, stop doing the War Campaign missions. You can come back to them once you have reached something like 119 and a half and finish leveling with those if you want. If you don’t use these missions to cap off your leveling journey, then they’re the first thing you’ll want to do once you reach max level.