I learned it as:

My father slew a kangaroo
He gave me the gristly parts to chew
Now wasn't that an awful thing to do?
To give me a chew
Of the gristly parts
of a kang - a - roo!

From my oldest sister, who I think learned it in Girl Scouts in the early 1960s in Colorado. Don't know if it's the same tune, tho...

You can actually sing it as a round if you're feeling silly enough.