I, too, am baffled.
Using the multi-city tool I can select PER-xHKG-SIN on CX. It prices and I get all the way through to the payment page until I get an error message. Several times this has happened. So I called Qantas and asked for some assistance.
The QF agent I spoke with went through the booking I was chasing and go to the same point I did and hit the same error. He investigated further and then determined that cx would not allow those two flights to be booked on the one itinerary. I could either book them separately (at a much higher cost) or travel on a JQ connecting flight from HKG to SIN (also, incidentally, at higher cost). When I asked him he assured me that it wouldn't be possible to book it as an award with any oneworld carrier.
But, bombshell, that's not true. After finishing the call I got straight on the phone to AA who booked exactly what I want, the very same itinerary QF assured me wasn't possible to booked.
Is this a problem with QF's booking system or an example of CX being nice to carriers other than QF? Is there any way around it?