Vetrade has covered it all pretty well. I would just add that this is a "Oneworld Award", not a RTW ticket (more on that later)... and:
1. As you are doing an economy ticket, I would suggest trying to book the trip online using the QF multi-city tool (which doesn't work all the time - especially for complex bookings- but worth giving a go). If you can't book it online, I'd support vetrade's suggestion of working out your rough travel plans... perhaps booking the first flight online as a one way classic award and then calling QF and adding all your remaining flights at once... which will minimise fees/charges.
2. The one flight at a time is generally done with premium cabins because they get snapped up quickly and QF waives the service fee for premium cabins. Booking one flight at a time for economy bookings would end up being very costly. Also generally economy tickets hang around longer than premium cabins.
3. As mentioned, each OW airline is different. Qatar seems to be pretty close to 365 days out.
4. This is where the terminology of RTW & OW Award confuses many. If you choose the RTW option on the QF site, you are trying to book a Oneworld RTW ticket... there are conditions on these tickets (like you need to fly around the world) and you can't book these using points. You are trying to book a OW Award, which is a ticket that allows up to 35,000 miles of travel, but does not need to go around the world. You can try and do dummy bookings on the QF site, using the multi-city tool... but as mentioned it suffers from many IT issues.
Also gcmap may be a good tool for you.
Vetrade is like the knowledge god on these bookings... so perhaps work out a rough plan and post it here for review/tips/suggestions?