How embarrassing!! This definitely rings a bell with me too (and Jeanie's game description) - from many years ago in Western AUSTRALIA. But was it from early Primary School (1950's), or 1st year Girl Guides (1960's), or was it merely from my little sister watching kids'TV in the early 1960's?? Who can tell ...

"What can you do, Punchinello, little fellow?
What can you do Punchinello, little man?
We'll do it too, Punchinello, little fellow!
We'll do it too, Punchinello,little man!"

Cheers! R-J