Hello
Lingo - welcome to AFF.
The most important bit of information the experts here will need is what type of OW RTW it is. If it's in economy eg fare basis MONE (M is the fare class), then AAdvantage may be your best bet. You can do a Platinum Challenge, which can get you to AA Platinum (OW Sapphire same as QFF Gold) in very short order. You then increase your miles earnings once you qualify, and become eligible for lounge access during your trip.
Some really good reading here:
FewMiles' Unofficial Guide to American Airlines Advantage - look in the "Undocumented" section for the Platinum Challenge.
However if it's in Business eg DONE or First eg AONE, then it becomes a lot more clouded. A well structured DONE in QFF will get you to OW Emerald (QF Platinum) more quickly than with the other OW FF programmes.
Do a search on the
FlyerTalk OneWorld Forum for a lot of really good tips on routing etc to maximise miles and status credits, and find out more about the various OW FF Programmes.
For example - if you're on a business class RTW, the flight from SFO-BOS will earn 150 QF Status Credits - that's because the trip is just over the magic 2700 miles mark, and you are put in first class due to AA not selling business class on that route. (US domestic first class is about equivalent to Australian domestic business class
)