This song is listed in “A Prairie Home Companion Folk Song Book” with the tune as “‘Fugue in G Major,’ by Bach.”
But I can’t figure out how you would possibly fit the lyrics to that melody as it isn’t very distinct or easy to follow.
Here are the lyrics:

I like tea, coffee, milk, and whiskey too,
But most of all I like a milkshake
Milkshake, milkshake, I like a milkshake
Milkshake, I like a malted milk

There is no recording or reference to this song online that I can find.
My best guess is that they said G Major by mistake and they actually meant to say “Little Fugue in G Minor” by Bach, because it fits that melody pretty well.
I’ve probably just solved my own mystery, but I’m posting this just in case I’m wrong, or on the off chance that someone else tries to search for the song like I did