You will have to do the quest with your racial trainer. If you're night elf, you must talk to the hunter trainer in Dolanaar who gives you the quest to talk to a hunter trainer in Darnassus. If you're a dwarf, it's the trainer in Kharanos and then trainer in Ironforge. This goes with all class-specific quests, in that usually you can only get them from your racial trainer in your capital.
Sorry to keep banging on about this but I spoke to the trainer Kharanos who put me through a couple of quest training different animals and then directed me to Dolanaar. When I went to Dolanaar the quest was ready to be handed in but after that nothing happened, I wasn't directed to another quest giver and so I returned to Kharanos. Since when no class trainer has had any quest or spell to offer me.
I suspect that this quest line was bugged for me so I am a little unsure what to do next. I don't really want to re-roll anther character just to see if the problem repeats itself.
