Here is a version from 'New Zealand Folksongs - Song of a Young Country', ed. Neil Colquhoun, 1972. Has a similar tune to that sung by Quinn. Collected from Dorothy Hueston in the early-1950s:
'Little Tommy Pinkerton'
Little Tommy Pinkerton the fat boy
Went to see his uncle Brown,
And when he was leaving his uncle gave him
A brand new half-a-crown.
Tommy felt very thirsty,
He went to the very first shop,
Had six lemonade and a dozen ginger beer.
Then there came a great big pop!
More work for the undertaker.
Another little job for the tombstone maker.
At the local cemetery they are very very busy
With a brand new grave for Tommy's fragments!