According to the following QF does interline with AC
https://www.qantas.com.au/agents/dyn/qf/news/200612/1255
I expect it's still current. As others have said 1:45 is enough time at SYD if you've checked in for both your QF and AC flights at MEL. Also your bags will be tagged with International Connection tags in MEL, so all you'd need to do is get yourself onto the bus between T3 and T1...
There are two separate facets to interlining. One is baggage and the other is boarding card. Qantas will interline bags with more or less any airline that uses one of the major airline reservations systems. Weather it is on the same booking is irrelevant, so long as you can show them your next flight they can enter it on the system and generate the baggage tag. The Qantas website says the cut off for passengers on domestic flight connecting to intenational is 45 minutes.
However they don't issue boarding passes for all airlines they interline bags to, regardless of which alliance they belong to. For example Qantas can issue boarding cards for Singapore Airlines, but not for Thai airlines. So if you have the situation where they can check your bag through, but not issue you a boarding card, what you need to do is get the transfer bus (showing your Qantas domestic ticket and itinerary for you international flight), then when you get to the international counter you go to the check-in counter of your airline, tell them you came off a domestic flight and Qantas checked your bags though. You show them the baggage receipt they enter it in their system and issue you a boarding card.