The Antiseptic Baby (?)

I often buy boxes or folders crammed with old paper stuff -- maps, letters, photos, postcards, advertisements, programs. My initial examination is rather cursory but when I get the material home, a closer look often yields some fascinating stuff. And some is just plain weird. Take for instance, the four-page mimeographed folder of nine songs. The one that caught my eye is labeled "The Antiseptic Baby." I have no idea of its origin or meaning and Google was no help. I leave it to you to help me out. Here it is.
(My original post, copied from an old folded mimeograph sheet, had some errors which were brought to my attention by an alert reader. This is the correct version, with the proper title.)

"Strictly Germ-Proof"
(aka: "The Antiseptic Baby" )

The Antiseptic Baby and the Prophylactic Pup
Were playing in the garden when a Bunny gamboled up;
They looked upon the Creature with a loathing undisguised; -
It wasn't Disinfected and it wasn't Sterilized.

They said it was a Microbe and a Hotbed of Disease;
They steamed it in a vapor of a thousand-odd degrees;
They froze it in a freezer that was cold as Banished Hope
and washed it in permanganate and carbolated soap.

In sulphurated hydrogen they steeped its wiggly ears;
They trimmed its frisky whiskers with a pair of hard-boiled shears;
They donned their rubber mittens and they took it by the hand
and 'lected him a member of the Fumigated Band.

There's not a Micrococcus in the garden where they play;
They bathe in pure iodoform a dozen times a day;
And each imbibes his daily rations from a Hygienic Cup -
The Bunny and the Baby and the Prophylactic Pup.


Prophylactic: disease preventing
Permanganate: a salt of permanganic acid
Carbolated soap: a salt of carbolic acid
Micrococcus: Spherical bacterium usually found on the skin of animals
Iodoform: compound of iodine used as an antiseptic.