Can I ask why the "rabbit, rabbit"? I keep seeing it on the first of the month, and I'd love to know the background.

I don't know the origin! My mother's side of the family always said it on the first of the month; it is supposed to be the first thing said on the day, like a greeting. (I associate it with my grandmother first and foremost.) I assume it's a luck superstition, but I actually have no idea why rabbits rather than anything else, unless it's the same line of thinking as feet.