Firstly, I will assume your points are with Qantas and not another airline.
What class of travel and how many people travelling together?
TravelLover2006 said:
When I arranged my family RTW holiday using QF FF points (planning started about 3 years ago, trip was May-Aug 2004) I started by looking at the award fare rules and how I could best fit in my desired destinations. Then I used the on-line availability tools to find flights with award seats available around the dates I wanted to travel. Then its time to call the airline and start making reservations.
Note that availability will be the biggest issue if you do not hold Gold or Platinum FF status and hence have access to greater availability.
OneWorld Award rules at a glance:
You can have up to five stopovers. A stopover can also be a "surface sector" where you arrive and depart from different places and perhaps drive, train or use other transport between these places. This is particularly useful in Europe where you can easily travel by Eurail Pass or in the US by rental car or even train.
A stopover is a break in the journey of more than 24 hours. So you can spend up to 24 hours in some places and still only be seen as a transit. This takes careful planning. We did this in DFW where we overnighted and met with friends for dinner before departing the next day in under 24 hours. We did the same in HKG on the way home and had a day of sightseeing before departing late the same night.
You must use 2 non-Qantas OneWorld airlines, but that will not be a problem for your itinerary as you will need to use LA trans-Pacific and BA, IB or LA to Europe, and BA to Africa.
Fees and charges will shock you. Be prepared for many hundreds of dollars per ticket.
Be prepared to spend a lot of time on the phone to the res agent looking for availability etc.