Don't you count Air France,KLM or Lufthansa as European airlines any more ?!?!
None of those flies to Australia (although they do codeshare on other carriers).
Two stops minimum ?? From Europe ??
If you fly from LCY, you will have at least two stops - one in Europe, and one in Asia or the Gulf. From LHR or LGW, you can do it with just the Asia/Gulf stop.