I think it depends what you have for breakfast - you shouldn't brush your teeth immediately after eating fruit or fruit juice as it damages the enamel. I brush, gargle, a polish first thing, then have a smoothie and then have chewing gum when I leave the house.
I would imagine if you have toast or cereal it would be ok to brush after eating.
I happen to like mint coffee. I used to smoke menthol fags before I gave up and whilst at work I was lured into trying a mint latte which I loved and then ran out and bought a pack of menthol fags because it reminded me of how much I loved them.
If you only want to do it the once then clean your teeth after breakfast.