It's a humourous take on the 'pistols at dawn' method of settling disputes between gentlemen in years gone by. A gentleman who was insulted or had his integrity or honour slighted, was entitled to satisfaction, by duel - often with pistols. The two would stand back to back, walk ten paces, turn and fire - the winner being the one, if any, who hit his opponent, but was in turn missed by him.
By tradition, a duel took place at first light - pistols at dawn. In modern times, some ladies have been known to settle disputes by a quick wack at the opponent with a handbag, and a mixture of the two - ancient and modern, would be 'handbags at dawn'.