If you do not see ANY world quests on the map, you still need to unlock them. You should have a quest from Khadgar that says exactly that and you will need to raise a few factions reputation to open up world quests. It's not hard though, questing through all 4 zones will get you there easily.
If you however do see world quests on the map, but not a single pet battle world quest, then this might be a filter issue. Check the filter settings on the map because you can turn on/off certain world quest types there.
Hope that solves it for you and good luck out there