You said she does so much though so what is it these famous people do who are supposed to be the head of a country?Not a lot as Paul Daniels used to say.
I kindly refer you to google.com, which will aid you in your quest to find out the Queen's duties, as well as other heads of state. You'll probably find more information on there than from Mr Daniels who's vocal chords don't work so well these days.
My apologies for stirring your emotions so early in the morning, Mr Rambo.
Mr Timbo can only work Google when it suits.