Hrothgar, if you go here Little Willie you will find more poems that will give you the idea. To be a "Little Willie" a poem must be macabre, and careless with life, especially the lives of children, and then have a surprise end, especially one with a bad pun in it.

Willie pushed his sister Nell
Into the family drinking well
She's still there because it killed her
Now we have to use a filter.

Probably these are most closely related to Tom Lehrer's Irish Ballad (Rickety Tickety Tin). Wonder if this is where he took his inspiration?
Blessings,
Barbara