I love the musical "Showboat" and played an old 78 to death one weekend. My son (9) went around proudly singing:
"Old Man River
He don't wear cotton" to which was added:
"He wears polyester
And it smells rotten..."

Does that count as a song written in response to a child's observations?

I was an unbearably cute child. At about three, at a family outing, Aunt Ruthie offered me a hot dog. To which I replied "I want a double-ender". (They always gave me half a hot dog because I was little.) She got $5 from the Daily News for that one.