It's a set of The Butcher Boy, also found under such titles as The Brisk Young Sailor (sometimes Soldier) and so on, so it wasn't composed, as such, by anybody in WWII; but it's interesting to know that it was current in the forces at that time; thanks for posting it. Which country's army was that, incidentally? I expect you mean the US army, but it's as well to be sure.

The song family is large and complicated; for instance, in the version above, some of the Butcher Boy narrative has been lost. In some, indeed, like Died for Love, hardly any story remains at all in many cases. There's a list of links to related material here and elsewhere in the thread  I Wish, I Wish, which you may find interesting. Links there to DT files no longer work since the site re-vamp, though.

There are three 19th century broadside examples at  Bodleian Library Broadside Ballads:

The Butcher Boy

Compare also

A Brisk Young Sailor Courted Me