Well, my ancestors came from Russia, and spoke various German dialects, so there isn't a drop of Roma in these veins. However I perform a variant of this song under the title of Black Jack Davey. Mine borrows heavily from versions collected in Virginia, and one recorded by Woody Guthrie.
I understand that the song came from Great Britain, and appeared about the time of James VI of Scotland, aka James I of England. While he was on the Scottish throne, James decides to kick all the "Egyptians" out of Scotland. One of them, whose name is supposedly Johnny Faa defies the order, and in some versions never leaves Scotland, or in other versions of the story returns to Scotland. Eventually the Law catches up with Johnny Faa, and they hang him. The songwriters of the day got hold of the story, and in the end we have our Whistling Gypsy Rover, or Black Jack Davey, or Gypsy Davey.