My limited experience suggests it's 140k points and QF told me it can be done online to avoid the 2.5, surcharge (although I'm not sure how). More importantly, however, the classic RTW Y award permits only five stops. Anything more and you're then looking at a whole new itinerary - that is, it's not possible to add on another sector using points. Put another way, the five stops are untouchable - that's it.
Therefore, the suggested itinerary above won't work within the 142k. That said, the routing maxes out at the five stops in North America where point to point flights using points are reasonably priced and, aside from that, there are a multitude of carriers in the US, including several low cost carriers that may well assist.
It's late at night for me right now but having had a quick play with the itinerary, my first suggestion would be: PER-HKG-CDG-DFW-LAX-HNL-PER.
Provided this revised five stop itinerary is permitted under QF's rules (I think it would be), the remainder of the itinerary could be completed by using FF points (on tickets separate than the RTW one) or pay using any number of airlines.
For example: LAX-LAS (very cheap, from memory, on AA and some people even prefer to hire a car). Alaska Airlines fly LAX-SEA and possibly LAS-SEA. That leaves SEA-DFW which can be done easily on AA. If you end up there, it's another easy AA flight back to LAX. And finally, Sydney. Well, that one may have to miss out on this trip, or simply do a return Y award PER-SYD for 36k.
My suggestion would be to use
Great Circle Mapper to determine the distance between the cities that aren't going to fit into your five stop RTW award, then go to the QF website and find out how many points are required for a journey of x miles.
Please report back on your thoughts on everyone's advice and what you're thinking now.