Yes, those ingredients were in the Irish Coffee (except the redhead which is a great idea) I thought I liked best which was from Uno's.  The bartender told me it had Jameson, Irish Mist, and a bit of Creme de Menthe crowned with whipped cream.  Generously sized too in a 12-oz glass mug.
I tried that at home and experimented with variations, but nothing quite matched what I considered the essential Irish Coffee taste.  Then one night I made a mug of my usual Melitta Decaf (yes, decaf) and added only a pony of Irish Mist.
Bingo!  To me, THE fabulous Irish Coffee taste with minimum fuss.  Couldn't be easier or tastier.  If you like Irish Coffee, I sure recommend you try one this way.  Can't lose -- if you prefer the other ingredients, just add them.