New Zealand has a woman prime minister, woman chief justice and a woman governor general (standing in for the woman queen;actually, I think she may have retired but the queen's still numera una, of course). Armed forces still run by men but as the PM refuses to send them to places like Iraq it doesn't matter.
And as far as I know, no chaos, though the male rugby team isn't feeling too good. In fact it's a very nice place, if you should ever visit it, clean and well run. I expect it'd be a big disappointment to you, though, claymore.