Parker Triumph at Melbourne
 

The Melbourne International Exhibition (the 8th World's Fair) was held from 1 October 1880 until 30 April 1881. I couldn't find a report of a shotgun shooting competition but firearms were on display.
The first "Queen’s Trophy" rifle competition was held at the "Victoria Ranges" in Williamstown.

https://photos.smugmug.com/US-Makers...r%201882-L.png

The 'Official Record' is here
https://archive.org/details/bub_gb_0csNAAAAQAAJ