Do not attempt to “Solo” this quest even if you can solo the dragons like I can easily do so on a frost mage.
If you’re not grouped you will not get a drop, I killed 275 Dragons before I tested out grouping to get a better drop. I remembered someone saying something years ago about the wow engine giving a bonus on drops if you are grouped.
Grouped up and 5 kills in even tho the partner was in another zone I got my Black Drake’s Heart drop.