Here are the quests of this Questline we know so far:
This Questline can only be completed once the Nighthold raid is unlocked!
You get one Quest every day but the date I'm posting this(Patch 7.1 Build 22989) it is still possible to get the next quest on a different character. So say you complete the quest on your druid you can still get a quest from the same pet from any of your other characters. Don't know if there's a limit though.
The Dungeon Quest can be completed on all Difficulties
Raising Your Direbeak
The Smell of Tauren or The Smell of Dwarves
Hunting Lesson: Rose Taipan
Allies in Stormheim
Direbeak Team Up
Dire Prey
Hunting Lesson: Tiny Apparition
The Unkindly Faction
Direbeak Bonding <<<<<You are here!*
Hunting Lesson: Golden Eaglet
Teamwork Lesson: Fenryr
Hunting Lesson: Stormstruck Beaver
Teamwork Lesson: Krosus <<<<<Nighthold! ? ?
Direbeak Reunion*[item=142499] can be bought from the clockwork assistant inside the toy shop("The Wonderworks") in dalaran(coords 44,46). The Robot is standing behind the counter.
Quest
Direbeak Bonding
Quest facts and objectives from the current retail game data.
The highest voted Wowhead comments for this page. They are community notes, not TheWoWDB comments.
The item is actually sold by the Clockwork Assistant robot. I was looking for the shopkeeper, who was not behind the counter, but in the corner to my left when I walked into the shop. The Clockwork Assistant was obscuring the gnome, standing in exactly the same spot. All this to say that if you don't find the false teeth in the inventory, you've most likely clicked on Jepetto rather than the Clockwork Assistant.
These are available in Legion Dalaran at The Wonderworks (42.37, 45.09) - it's the shop with the teddy bear sign diagonally across from the Violet Citadel. Clockwork assistant is just inside the door to your left. Fake teeth will be the last item in his inventory and cost 14g 53s.
Quest facts
The client quest POI data records no map location for this quest, so no map is shown.
Check whether you have already completed this quest
in-game: /run print(C_QuestLog.IsQuestFlaggedCompleted(44982))
Description
<Your direbeak hatchling puffs up its feathers and growls at you in a display of dominance. It seems unhappy with the results, as you are not cowering in fear. It might like to dress up like a grown-up falcosaur and try again.>
Community notes from Wowhead · 9 comments
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Reward details
Items you receive
Item facts are the current retail client’s (ItemSparse); the specialisations for a pick-one item are the ones the Blizzard quest API lists; faction and currency text is the client’s own. Lowest listed price = the US commodity auction house now.