I am at the same problem! I just turned level 78 myth and went to Cyrus Drake, but I did not see the quest icon above his head. So i found out you have to do Wintertusk to get the pet. Hope this helps!
Here are the requirements for getting your level 78 pets. This requires you to do Grizz and WinterTusk. If these have not been done, it will prevent you from obtaining future spell and pet quests. "Nordrilund Exposure" to be done in order to get your level 88 spell quests in Azteca as well.
There are 3 requirements to meet to be able to accept the starting pet quests from your school professors in Ravenwood, Nightside, or Krokosphinx. Each school has a different quest! You must be a minimum of level 78 You must have completed the quest "Nordriland Exposure" You must have completed your school’s level 58 spell/pet quest from your professors. Fire must have completed the quest "Like a Phoenix" from Professor Dalia Falmea Ice must have completed the quest "Wings of Valor" from Professor Lydia Greyrose Storm must have completed the quest "Egg of the Storm" from Professor Halston Balestrom Myth must have completed the quest "Frog in Your Throat" from Professor Cyrus Drake Life must have completed the quest "Ready to Hatch" from Moolinda Wu Death must have completed the quest "Century Egg" from Dworgyn in Nightside Balance must have completed the quest "Balancing Egg" from Alhazred in Krokosphinx Once you meet all of these requirements, then you can go talk to your professor about getting a new pet!
Fire Wizards will receive the quest “Firestarter” from Professor Dalia Falmea Ice Wizards will receive the quest "Misery" from Professor Lydia Greyrose Myth Wizards will receive the quest “Eyes of the Dragon” from Professor Cyrus Drake Storm Wizards will receive the quest “Hearts in Atlantis” from Professor Halston Balestrom Life Wizards will receive the quest “The Green Mile” from Moolinda Wu Death Wizards will receive the quest “Bag of Bones” from Dworgyn in Nightside Balance Wizards will receive the quest “It” from Alhazred in Krokosphinx
wizard how come I didn't get the quest for 78 pet
student but have you tried going to your teacher? If not good luck finding it 
wizard and i didn't get the quest too 
wizard and I to have the same problem i never got the pet quest. can you tell me why or can yo fix it for us and me?