Willy
Source: World Event. He's slightly evil but extremely narcoleptic. Keep him away from critters! Magic type. Maybe its just me but I see a little dirty humor in his name and the fact he's a one eyed monster.
Willy is a one-eyed pet obtained by completing the Children's Week world event quest chain in Shattrath.
Guide awaiting review
Start Children's Week quest
Visit Orphan Matron Mercy at 75, 47.6 in the Lower City of Shattrath to begin the Children's Week quest chain. This event is only available during the Children's Week world event.
Complete three orphan quests
Complete the three quests in the Children's Week chain. One quest involves visiting Hch'uu and the Mushroom People at 44, 64.2 in Zangarmarsh and at 19.2, 51.3.
Complete two additional quests
After completing the three main quests, two more quests will appear at 89.5, 50. Finish these quests to unlock the pet selection reward.
Choose Willy as your reward
Complete the final quest at the Shattrath Orphanage to choose 
Sleepy Willy as one of your three pet rewards, along with other companion pets like Egbert and Peanut.
Tips
Completing the full Children's Week quest chain grants approximately 1500 Lower City reputation in addition to your pet rewards.
Willy occasionally shoots a beam from his eye at critters, so keep him away from them if you prefer to avoid this behavior.
