I'm not including wild pets in this guide as there are already others that do a fine job. This is for pets obtained outside the pet battle system - there are surprisingly few.
How to actually kill him is still unknown. He has 75 million HP and applies a DoT that deals 25% of your max HP per second and reduces healing by 100%. Pets (hunter/warlock) don't get the debuff and can very slowly wittle him down if the player doesn't attack him. Indalamar's Holy Hand Grenade is expected to be involved with this rabbit but no source has been found.
You can obtain 18 pets by this point.
Out-of-Game
Lucky Quilen Cub comes with the Digital Deluxe Edition or Collectors Edition of Mists of Pandaria.
Baneling comes with the Collectors Edition of Starcraft: Heart of the Swarm
Unknown
The following pets have been datamined but have no known source. They may end up not being available at all. Or they may be lost and should be wild pets.