Not related to any of the Marrowbones family, as the lyric isn't traditional, despite what it says at http://www.3pintsgone.com/lyrics/StValery/OnWeGo.htm.

Some details of the record from which that band learned the song can be seen at http://www.mollys.com/mollys/buy.htm, where it is stated that "This Is My Round (Apolkalips, 1995) contains 14 songs, all Mollys originals with the exception of two tradiontal [sic] tunes given new lyrics by Nancy McCallion". On We Go is one of those; there is no indication as to what the tune might be, or to where they got it.