PER-BNE-LAX-JFK-BCN-ATH-LHR-DXB-HKG-SIN-PER is only 10 segments & 29523 miles. (Miles from http://gc.kls2.com/) Not using the maximum 20 segments is almost treason on this forum. You have a maximum of 20 segments, so if you want to get more ff points/miles or QF SC’s (and spend more time in aircraft and airports) plenty of opportunity. Selecting flights distance to maximise SC’s is what many do.

You have 4 flights allowable in Aust with 2 stopovers. So after arriving back in Perth you could PER-ADL-PER or PER-ASP(Alice Springs)-PER for example any time in the 12 months after your first flight. PER & ADL would be the stopover. Your first stopover in PER could be 1 or 4 or 10 months or what ever and then a 1 week in ADL/ASP. Being from PER the transcontinental rules restrict your possibilities (unless you want to pay to get back to PER after using the 4 Oz segments)

Also note that on LONE4 flights with CX you get nil miles. QF Earning table
Could do PER-BNE-LAX-JFK-BCN-LHR-DXB-LHR-HKG-SIN-PER , with LHR-DXB-LHR all on BA and buying a separate flight to ATH (some flights in EU are very cheap). OneWorld validator will tell you what is allowable. (but the SC's & miles earned are not always correct as the software does not know what airline you are flying)

Buying your LONE4 direct from American Airlines in Sydney will be cheaper than buying from QF (either QF direct or from a travel agent). AA do not charge the fuel surcharges

Also do not ignore the option of joining the AA ffp and doing the Platinum challenge to get instant AA Plat (= QF Gold) depending on route and airlines flown. AA miles are worth 1.5 ~ 2.0 more than QF points. (Rewards need a lot less miles/points)

Now if you want to go one better, get a cheap flight to SIN, then Finnair (AY) SIN-BKK to buy a DONE3 or DONE4 (business class).DONE4 ex Oz approx $2500 more than ex BKK; ex CMB is approx $3,000 less than Oz (serfty post on another thread)