minstrel: Why Shouldn't My Goose?

[Yarrow, Patricia]

Greetings, all.

I was flipping through a vintage (early 20th century) book of songs for children and was surprised to note a slight but significant difference in the lyrics for the round, "Why Shouldn't My Goose."  Instead of the usual

"Why shouldn't my goose 
Sing as well as thy goose
When I paid for my goose
Twice as much as thou?"

The book gave,

"Why shouldn't my goose
Lay as well as thy goose . . ."

Which of course brought to mind the 16th-17th century English use of "goose" as slang for a prostitute.  Does anyone know the origin and age of the round?

Somehow I don't think this is a children's song . . .

Vivien