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Of course not . But best way is to join BA not to redeem using BA Avios - but instead just to use their search engine to find the flights you want - then call QFF to book them. Saves a lot of trial and error over the phone with QF.
To join BA you need an address outside the SW Pacific - If don't know anyone overseas - a hint is to accidentally select the wrong country with a different country on the drop down list that is very close in spelling to Australia...
Can you pay over the phone with Qantas giftcards to avoid cc fees?