A wild rabbit, not someone's pet!
I always feel a bit naive when I notice how surprised I am when I see a dog do that for the first time. My previous dog was 100% hunting dog and I remember finding a gutted possum in the backyard one morning and being puzzled about this for months because I firmly believed that there was no way my nice dog could've done that. Of course I soon learnt that she was very capable of that.
And now, because Banjo doesn't look anything like a hunting dog, I naively thought that she was just chasing the bunnies for fun. Until one squealed and was very dead. I felt quite bad about it.
I do consider rabbits to be in the same class as mice and rats, so I won't lie awake about it. I think the worst thing is always that realisation that I lost control over the dog for a while when she chased it, killed it and then spend a while enjoying her trophy (made worse by foster pup trying to get it off her). I decided to continue along the usual path for a few minutes and then called her from a distance and she came then.