Though I did notice that both Beasts of Fable, and the Pandarian Spirit Beasts quests are both available for me to pick up again from the quest giver despite them both still being in my log. Is that what's causing the issue? Because I wonder how many others are getting the same issue then.
Edit: OK, it updated finally after I relogged. Dunno if it was just lag causing the issue or if there's a small glitch or bug that sometimes causes you to need to relog to get that particular pet to count toward the quest..