Four copies in Bodleian Library, about 1850. All have the chorus as a single line,
Musha ring a ding a ra.

Four copies in American memory, about 1860. All have a four-line chorus,
Rack fal de ra
Rack fal de raddy, O
Rack fal de raddy, O
There's whiskey in the jar.

Warner Coll. (from thread 3116, Gilgarrah Mountain, posted by Liam's Brother)
Musha ringum durum da
Wack fol the daddy O (2X)
There's whiskey in the jar

I would guess (only that) that the chorus was a nonsense rhyme from the beginning.