I'm still working on an April/May 2027 trip to Europe on an OWA but currently can only find a routing via the USA both ways.
Little luck with QF metal and, indeed, BA and AA, but plenty of other airlines if you look, but they come with problems.
Fiji Airways does do some connections to LAX or HKG in J via Nadi to Australia, but you have to get to their gateway cities first, e.g., lots of availability in April in HKG-NAN-BNE with a reasonable stop at Nadi of only 2 hours.
Oman Air is similar, but you have to get to KL or SIN first. To be fair, if you are happy to spend 7 or 8 hours in Jetstar business class and it's not an OWA booking, it looks good; it is possible to fly LHR-MCT-BKK-BNE. Oman Air seems to have a good name, but their business cabins are small, so only a few seats seem to be released. There are plenty of First Class seats on offer, though.
Similarly Philippine Airways offers good connections out of Australia but not in Oneworld.
So, to be fair, you can find some QFF reward flights to Europe without going through the USA, but many do not fit in with OWA rules!