Hello again Flyertalkers!
Have been researching some more (thanks to your advice), and have come up with this first draft for our RTW.
I guess it's a DONE5 (?)
The plan is to make the most of the ticket (obviously

), and preferably fly with the best possible fleet. We'd like to alternate between visiting cities and beaches/relaxing.
Here is the itinerary as it looks now.
CAI-DOH-MEL-AKL-KUL-CMB-HKG-LAX-GRU-SCL-IPC-SCL-MIA-SKB-JFK-LHR-CAI
We will probably buy some separate tickets (+CPH-CAI-CPH of course) in Australia, Asia and maybe South America, so we get to see as much as possible.
All comments/questions are welcome!
Once again, thank you for your help!^