I had another play with the oneworld tool, I could not get it to locate the direct flight from AKL-HKG so have gone via Sydney and changed the route slightly.

Here is the route I am looking at now: lhr-doh-per-syd-akl-syd-hkg-bom-kul-nrt-hnl-lax-sjo-lax-jfk-doh-lhr (GCM)

Everything works OK in the planner until I get to JFK, it is not showing up direct QR flights from JFK to DOH and only 1 stop flights (thus adding an additional segment)? Any reason why this might be?