For a hunter's pet, the easiest one to get is level 12 The Kurken in Stillpine Hold on Azuremyst Isle, but you must have the Burning Crusade expansion to get there and the Beast Mastery talent to tame it. The Kurken was once tameable at low level, but that was removed and it was re-added with the talent requirement. The next easiest two-headed dogs to tame would probably be a level 69 Spawn of Uvuros in Shadowmoon Valley and level 61 elite Core Hound in Molten Core.
All these types of dogs are considered "core hounds" for the purposes of the Beast Mastery talent.
The types of tameable core hounds:
- Azuremyst Isle
- Level 12 The Kurken
- Upper Blackrock Spire
- The Beast (80K health)
- Molten Core
- Level 61 elite Core Hound (< 50K health)
- Level 59-62 elite Ancient Core Hound (> 100K health)
- Level 62 elite Core Rager (80K health)
- Boss Magmadar (800+K health)
- Shadowmoon Valley