"white rabbit! --    A phrase said, before saying anything else, on the first day of the month in order to bring good luck" -- Wictionary.

As always, there are several versions of the superstition. I was brought up to the one that you only say it [in the plural, BTW, as 'White rabbits'] on waking on the first day of the month in which your own birthday, or that of someone particularly close, occurs. My wife Emma knows exactly the same version; we both originated in N London, which may have something to do with it. We also have birthdays in the same month, so can say it for one another simultaneously.

≈M≈