Withers is a post-Cataclysm pet avaliable as a reward to the Quest: Remembrance of Auberdine. To do this quest you have to do around 30-40 quests in Darkshore including basic Lor’danel quests, Cliffspring Falls quests, Ruins of Mathystra quest and quests involving Grimclaw. You can achieve this pet around levels 15-20.
Withers is pretty big for a pet when you first summon it, than over time it “withers” and becomes smaller. To make it big again, you have to get it in water.