Barbarian Hero idea is better. I wouldn't want to see multiple killer rabbits in the world. I also don't think it it should be killable only by the Hand Grenade of Antioch. It should be a ~ 66 strength animal, so it is difficult but not impossible to kill (using an avatar are a high level recon hero), but the use of this piece of equipment (which spawns at the same time as of just before the rabbit) should mean instant victory over it.
The Killer Rabbit/ Holy Hand Grenade spawning shouldn't be triggered every game, it should be a random event that happens once in, say, 1 in 10 games.