The rule is that any OW airline is allowed to ticket any Oneworld product but the airline flying the first international sector must ticket it (if requested). The others can decline (and pass it to that airline).

Now, from a passenger standpoint, you might prefer one airline to do the ticketing over another. Most would prefer AA to issue the ticket (costs less), and QF is probably the last choice. Having it validated in advance is fairly important, look at how many problems there are with reissues much less with new tickets, and how long it takes to resolve them sometimes.