Yes, Steve's right about Desi's interpretation.
Should be:
Dum-de-dum-de- da-da-da-dum,
Dum-de-dum-de- da-da-da-dum,
Da-da-de Da-da-de Da-da-de dum--de
Dum-de-dum-de-da-da-da-dum

We have "Off she Goes" in one of our ceilidh sets, usually for the final (Orcadian) Strip the Willow: not sure about Humpty Dumpty having a great fall, but one of our dancers did, and broke not one, but BOTH wrists in one go!