The rabbit was likely a wild animal, so would not be missed or owned by anyone else. As long as it was definitely dead then you've done all you can in that case, short of calling the local council authorities to report a dead animal in the road, (this would be classed as roadkill). If it is still alive there are animal charities you can call that will come out and deal with it. (Such as the RSPCA emergency number.)

A pet though... although I admit I'm basing this purely on emotional reasoning, deserves a little more care. Someone could be left heartbroken/lonely and grieving over something that a vet could maybe fix if called in early enough. This would usually be of no cost to the driver, so it seems the decent thing to do.

If this isn't an option then again the RSPCA emergency line can help.