An interesting thing, I was a museum in the renowned Balboa Park here in San Diego, & it so happened that a feller was there visiting who is an Anthropologist. In looking at some ancient artwork, I noticed several rabbits decorating pieces of art. The feller said it was a symbol of fertility. I then asked him the Q re saying rabbit rabbit. He laughed & said his favorite old Prof (what an irony--see my original post!) told them while in University that it was the practice of women in ancient times at the beginning of the year, to pray to goddess of fertility-a goddess with lots of rabbits hanging around her, for fertility in the coming year. Over time, this turned into praying to rabbits & deities for fertility & good luck, & then the superstition of chanting or speaking the word rabbit on the day of the new year for good luck in the coming year.
He said that it is believed that British soldiers who were stationed in the middle east at the tail end of of the 1800's brought this back home with them.
I had to chuckle, because now I'm thinking that there might be many who say "rabbit rabbit" or "rabbit rabbit rabbit" who would not wish for fertility in any month or year. I, for one, am relieved that the fertility Goddess did not honor me with fertility!