I'd gone off to get the number and a graduate of the AA Plat Challenge steps in and gives all the relevant details.. excellent
Sequel.
The BA earning table is
here.
According to
Mile Markers' website (your mileage may vary), SYD/BKK is 4,680 miles (one-way); thus 9,360 miles in total.
But as earning on BA's V class is 25% of actual flown mileage and 50% EQP's
on mileage earned; then you should earn 2,340 miles in the AA program and 1,170 EQP's (or 12.5% of actual mileage flown). This is insufficient for the Gold Challenge requirement of 5,000 EQP's...so as
Dave Noble commented above, do you have any more flying in the 90 day period...
Of course, if you could change to the QF codeshare flight number, V class would earn you 50% mileage and 100% of mileage EQP's (thus giving you 4,680 miles and the same number of Q-points, still short but a domestic flights could push you over - would be better taken prior to your trip and making you Challenge have to start earlier).
Even better would be the possibility of changing to the AA codeshare, which would give you 100% mileage and EQP's, easily meeting the Gold Challenge and being 640 short of the Platinum Challenge level (10,000 EQP's)...if you fly some domestic QF flights prior to your trip having already enrolled for the Challenge, that would push you over by the time you return (and give you a 100% mileage bonus on the BKK/SYD flight). If you are able (assuming it's cost effective to change the flight numbers), I'd enrol for the Plat Challenge.