Hi,
There is one birth registered in QLD for 1893 for Catherine with parents Margaret Kelly and John Edward DUNNE.
There are 2 birth registrations in NSW that could fit your couple.
21378/1883 DUNNE Rose E
23277/1884 DUNNE John Edward
Registered at Inverell, not far from Queensland.
Do you know the names of Margaret and Johns' parents please?.
Leanne