Make sure before you try and complete this quest chain that you have already done the start of the Warbeat Kraal questline, to which this is the concluding quest line to it that was just added in 8.2! See top comment at: The Orphaned Hatchling
for all the info on the first prequel to this quest line.
The very first quest in the chain to start all of this is "The Orphaned Hatchling", contrary to the first and top comment on here. Which states The Trust You've Earned is. That quest is just the start of the new sequel chain added in 8.2.
Small edit: I started the very beginning of the questline (the quests that were out in the release of BFA) and was able to do all of those quests in about 30 minutes. Doesn't take long and you can do them simultaneously in one day, until you get to the 8.2 set of the quest which starts at The Trust You've Earned. BUT you do have to log out and back in once you complete Naptime just to get the direhorn to finish his nap! I otherwise do not know how long he will take to finish his nap.
All of the quests for this questline added in 8.2 can only be done once per day.