Any suggestions/tips on booking Round the World business class using FF points?

I have started to book flights for a 2017 RTW business class holidays using our Qantas points. So far I have booked Syd-> Joburg, own way to Naoribi -> Lisbon. From there we wish to go to Europe and then on to New York, San Fran, Miami and Mexico -> Sydney.

Our problem is trying to avoid London and British Airways. Each time I ring Qantas (6 hours later) I am still no further ahead. Any suggestions?

Your best best to avoid BA fuel surcharges and the UK departure tax is to avoid heading to the US from the UK. This means you will need to find award flights on an alternative oneworld airline. Possible options are Finnair (from Helsinki), Iberia (from Madrid), Airberlin (from Berlin) or American Airlines (from multiple places). Award availability will depend on when you’re flying, how many people etc.

You can search award space for most these airlines using the BA or Qantas websites.