I think many of the people who are currently trying to complete the pilgrims bounty achievements are stuck with this as the last thing to do, high competition, slow respawns and a short debuff duration really make this a hell.
Other guides have already covered where best to farm them as both alliance and horde, so I will not go over that again, there are just another 2 tips I want to give:
1. the hunters Track Beast abilitys actually also works for turkeys, and since they are one of the only beasts with yellow markers around elwyn/tirisfall, this makes it really easy as a hunter.
2. the item Tracker Snacks - Item - World of Warcraft gives you the ability to track beasts, and thus turkeys, which should really make things alot easier aswell