The only problem I can see with the two itineraries is the AYQ-ADL sector - there are no QF flights. According to the QF web site the only flights out of AYQ are to PER, CNS, MEL, SYD and ASP.
Which itinerary is preferable? - well only you can say
IIRC the AA GSA in CPT is Mindpearl - so if you search for that in this forum you should find everything you need.
From what I've read in this forum, the best option for you is set up the trip using the AA RTW desk and then get it ticketed by the local GSA (saves on fuel fines).