The challenge you will face with a wire low enough to get rabbits is grass growing up shorting it out. Some of the stronger electric fences can burn off grass as it touches it. Alternately you will probably have to weed wack it on a regular basis. Cows, deer, dogs and such soon learn to stay away from an electic fence once they've been zapped. I don't know about rabbits though. They breed a new gang on such a regular basis that I think the fence would have to run 24 / 7.