I'm from Australia and the version I know is:

Aunty Mary had a canary; she also had a duck.
She took them behind the kitchen door to teach them how to...
Fry eggs for dinner, fry eggs for tea.
The more you eat, the more you drink, the more you want to...
Peter had a boat; the boat began to rock.
Up jumped Jaws and bit off his...
Cocktails, ginger ales, 40 cents a glass.
If you don't like it, shove it up your...
Ask no questions; tell no lies.
I saw a copper doing up his...
Flies are bad; mosquitoes are worse.
This is the end of a clean country verse.