Although the word doughboy became popular in WW1 when referring to a member of the US infantry who I presume to suggest were only too happy to get in scrap the word first came into existence during the US civil war. There are various possible derivations. It could refer to the large doughnut sized button on their uniform or the "dough" used on the cross belts or even from the word "adobe".
As regards a punch, Pudcat, at a guess I'd say it has to do with the American character, the Pillsbury Doughboy. He's a round, flabby, white cartoon-figure and it seems to be obligatory to plunge your hand into his stomach. I believe I recall Homer doing precisely that in one episode of 'The Simpsons'. Maybe that's where the punching idea came from?