LC: "I take it though that as 'Daisybell' has said she's at an all girl's school, then she's either at a Girl's Grammar School, or a Private girl's school, because I don't think we have Girls only school in the State system, do we?"

I think Daisybell specifically stated that she attends a single sex *State School* and not a Private School.

There are still state supported faith schools - which are also most likely to be single sex. My Mother went to an all girls Catholic school.