I also found this:

PLANT A LITTLE GARDEN IN YOUR OWN BACK YARD : DIG FOR VICTORY
Words by Walter Hirsch & Bert Lewis, music by Walter Leopold.
Chicago : Forster Music, ©1917 [It was reprinted in 1942.]
"Introduced and featured by Jan Garber"
First line verse: Plant a little garden in your own back yard where the green grass used to grow.
First line of chorus: I've been reading in the papers that the price of food is high.

Copies of the sheet music are held by Kansas State University, Bowling Green State University, Brown University, and the British Library.

You can hear the following recording at YouTube. The arrangement is very reminiscent of Spike Jones.

PLANT A LITTLE GARDEN IN YOUR OWN BACKYARD
As recorded by Al Trace and his Musicians, 1940's

Plant a little garden in your own back yard.
There's so much that you can grow.
Plant some nice potatoes,
And some red tomatoes.
Buy a rake and hoe.
You'll have plenty for the folks and children by and by.
You should worry if the prices go up to the sky.
Take my good advice and plant a little garden in your own back yard.

Plant a little garden in your own back yard.
That's the least that you can do.
Phone your cousin Annie.
Write and tell aunt Fannie,
And your grandpa too.
I'm a little moron, but I'll help win this war.
I'll keep raisin' more an' more an' more an' ohhh—
So get a rake and hoe,
And get some seeds to sow,
And dig! Dig! Dig!