To find these flights in ITA Matrix
Choose Roundtrip
Origin - MIL
Destination - SYD
Routing Codes - <blank>
Extension Codes - f bc=i; -cabin 3; opairlines qr ul
See calendar of lowest fares
Start Date - Choose a starting date
Duration - Set a trip duartion
Stops - No Limit
Extra Stops - No Limit
Cabin - Cheapest Available
If you don't care about segments operated by AZ, AF, LH, then set the Routing Code to "UL+" and you don't need to include "opairlines qr ul"
EDIT
There is lots of availability through October 2024. Here's screenshots of ITA's calendar for April through December.
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