I presume you mean :how do I get RTW quotes (using my points) on a trip PER/SIN/LHR/JFK/LAX/SYD/PER. My understand is that the only way is to ring up QF Res and find out - subsequent to 25 May, it has become harder for pax to "do it themselves".
Tips:
PER/SIN: you have the daily QF 77 or less frequent QF71 or QF15
SIN/LHR: you have the daily QF31 of less frequent QF15 or QF 9 (or codeshare BA flights QF319 or QF387)
LHR/JFK - look for QF codeshares on BA flights
JFK/LAX - look at using QF108 (JFK/LAX) on Sun, Wed & Fri (or any of the multiple codeshare AA flights)
LAX/SYD - there are a number of flights daily (QF108 or QF12) or the less frequent QF8, or even QF176 (via BNE).
RTW fares can be found
here - try an LONE4 (L class, on Oneworld airlines, 4 continents) from $2,979 to $3,239 (depending on when you are travelling).