As hinted by NItroX, I'd definitely go London - Johannesberg - Perth then Perth to Darwin over the standard route which probably involves stops in Bangkok or Singapore.

Not sure I'd want to be packing a rifle through Singapore and any nonprescription medicine in the luggage might really upset the locals. Also given the potential alternates along that route, a problem could result in landing in some other Asian country unfriendly to passengers travelling with firearms.

QANTAS has their schedules available online as well as in downloadable pdf files and a small program called QANTIM for download that allows you to click and drag routes on a world map and pull up flight numbers and schedules. All the downloads are on this page:

Flight Info - Timetable - Timetables
http://www.qantas.com.au/flightinfo/do/dyn/ScheduleSearch;flightinfo=C7KcZ6JlBT6OgM2qwOXxIuoKN3mv752MLBYotBApEB1pEN7VrZ8Z!1094128619

Richard.