Although Delta does not have a codeshare any more, it is quite possible to fly JFK-LAX-SYD-MEL with the final leg on either VA or QF. Delta also has a partnership with Rex, although that may not be reflected in the fares they have filed yet. I used ITA Matrix to force the routing.

Many of the other SkyTeam carriers that fly to MEL are Asian like CI, MF, GA, and VN and have very limited schedules right now, and ability to transit.

As ​​​rylan pointed out, it is possible to book AF/KL through SIN with the final leg on QF.