You can not leave the country of origin twice, so originating in the UK is a bad choice for RTWs (since LHR is such a key hub for Oneworld.) Originating in the UK is also very expensive compared to other origin points. For the time being ARN is the cheapest business class origin point in Europe, so changing your itinerary to ARN-LHR-DXB-LHR-JFK...MRU-LHR-ARN would be the easiest thing to do. There are other approaches as well - CDG-AMM-DXB for example, but remember to leave a Europe segment available at the end to get back to your origin point.

For a DONE4, I'd check to see about D availability on some flights - I think maybe SYD-ZQN is only Y but not sure; you could use CHC as an alternate I suppose. Otherwise, no problems with the route.

Edited to add - welcome to FT!