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Korendirs advice worked like a charm for me. The hare does not seem to spawn immediately after killing/battling the rats, but I always found some sooner or later, sometimes respawning in the very same spot I had fought another in the same cycle.
Apparently the rats respawn only once all possible hares have been dealt with, so when their corpses can be seen, a hare could possibly be spawning somewhere. But: Hares do eventually despawn, so don't take to much time.
Still need a rare one though.