Wild rabbits can be particularly challenging to Photograph. Most of the time rabbits will hop into nearby shrubs. If you shoot at a shutter speed of a 1000 sometimes depends on the lighting you will have to shoot at a higher iso this causes there to be more noise in the image. If you are lucky and the rabbit freezes for a couple of moments then you can capture them at a low iso and a low shutter speed. I like to keep the shutter speed at at least two times the focal length. Like wildlife bird photography fast moving wildlife can be a challenge to capture.