I should think the street was named for the church/cathedral rather than the other way around. Saint George is the patron saint of England, and it's an English (Anglican) church.
SLWA (posted to Facebook): 303444PD: Looking west along tree-lined St George's Tce, with groups of people in the foreground and the Pensioner Barracks just visible in the distance, c. 1863. Photographer not named. It looks like the work of Alfred Stone.

SLWA (posted to Facebook): 303442PD: Soldiers in formation [?] in front of the Pensioner Barracks, Perth, c. 1863. Commandant John Bruce at the front on the right.




SLWA photo 011486D, Alfred Pickering, 'Old Barracks'



Simon Nevill's conjectural sketch map: 22.
Neville, Simon J. 2007, Perth and Fremantle: Past and Present, privately published, WA.
Garry Gillard | New: 7 July, 2021 | Now: 19 November, 2023