World quests may not be a reliable way to power-level your pet since experience can range from 380 during a Rocko battle to 5,060 for the Ominitron Defense System. Thankfully, there are at least 10 battles you can successfully use to level a pet for your Family Familiar and Battle on the Broken Isles achievements. Click on the image to see each pet strategy.
Andurs offers a decent amount (2,090 XP), though not quite as much as my top 10 (5,060-3,715 XP) listed above.
The Draenor circuit is still my preferred way to level new pets and will probably be for some time to come – 400 Draenor battles to go