Hey there! OK, the Head Boy and Girl Duties.

The only references I can find is when Hermione says that the prefects get instructions from them on the train, and also when Percy and his fellow Head Girl keep an eye on the students after Sirius's break-in.

What duties do you think they have?

In most fanfiction, they patrol in the evenings and plan balls, Hogsmeade weekends, etc.

Thanks!
~Annie