I’ve had to do similar before. When I was 16 I was learning to drive with a friend’s dad out in rural Australia. There were a bunch of ducks crossing the road at one point; I stopped to let them pass, but after they moved on and I started rolling forwards one duck turned around and tried to attack the car, resulting in me hitting it. I couldn’t even look out the rear view mirror at it but my friend’s dad did, and told me it was still alive but very mangled. He gently told me to reverse back over it and keep on driving, which I did, and then we drove in silence for the next fifteen minutes.
I felt absolutely awful about it (and still do, despite it happening almost 2 decades ago) but I know that leaving it in the road dying slowly would have been a far worse fate.
I hope you take some solace in the fact that you did the right, albeit difficult, thing for that rabbit.