Nelthara

To be almost certain you'll get the initial Our Destiny quest for this Dracthyr/Evoker-specific pet to pop up on 10.1.5's release and later on:

Have your Dracthyr leveled up to 70, specialize into Augmentation and zone inside of Valdrakken (i.E. by running down the stairs from "Seat of the Aspects" until the zone is showing "Valdrakken", it should only take a second for the quest to pop up after that.

While it doesn't matter what your spec is when you've got that initial quest, for the final quest Augmenting a Dragon, it's mandatory to be specialized as [spell=396186], a little encounter requires the usage of [spell=395152] and [spell=360827]. (when I did that, the quest didn't mention that).

You're here because you're doing wow secrets and Nelthara is one of the pets right? OK, so I never got this quest on my evoker, but after reading the comments I switched to aug and got the quest as soon as I zoned in to SW. Then you just have to fly to Forbidden Reach and do 2 simple fast quests to get her!