The Killer Bunny appears after the player character has killed 30-35 rabbits. It is inadvisable to challenge this opponent before reaching level 20 because the Killer Bunny is level 22.
The Killer Bunny will not go in water. Kill the last bunny right next to a stream, step in the stream or jump onto a nearby rock that can't be normally climbed and take your time killing the killer bunny to unlock the Bunny Bagger achievement and get 3238 experience.
There are multiple references to the Killer Bunny elsewhere in the game, mainly in books. The first possible place to hear about the Killer Bunny is from the diary of Brave Sir Robin, from whom you get The Greater Hunter quest.
If playing the DKS version, save just before killing Killer Bunny, as the loot bag can contain up to 2 random items of Elder quality.