It will only spawn once. I'd guess it should hang around until you get back to it, but I don't have a save before then to check if it would despawn.
I did have enough time to jump away from the killer rabbit, since it usually couldn't one hit kill me. If it spawns where the last rabbit was, then taking it out with a bow or magic would give you extra time to get away or jump/climb to higher ground.
If you make sure you don't have any poison auras on jewelry, etc, then it shouldn't be too hard to avoid killing rabbits (don't run past them quite close, or your character can rarely, but fatally, kick them).
