The Wyoming State Tribune: A dread occurrence in headgear. June 12, 2018.

The war raged on and the Army had authorized the "rabbit cap".

I've never heard it called that, but I know what they meant.  They meant the Garrison Cap, or Overseas Cap.  That useless piece of headgear which every soldier was afflicted with in varying degrees for decades, and which is still worn by Veterans Organizations.

World War One soldier wearing the complete assortment of wartime gear, including the garrison cap, puttees, and wartime roughout "Pershing boots".  He is carrying the M1917 Enfield Rifle, rather than the M1903.

They'll be more on this in an upcoming thread.  Probably more than one.  Suffice it to say, the cap had no real virtues other than that its flat and doesn't take up any room if you aren't wearing it.  Based on a French pattern, it sufficed for some sort of hat for men who were wearing helmets in combat, and therefore had to keep their campaign hats somewhere while at the front, which was a pain.

But it was around forever.