Welcome to FT beccampbell!
Your question will most likely soon be moved to another forum (most likely the "Qantas Frequent Flyer" forum) by a helpful moderator so that more of the right people will see it, but I can answer one of your questions now:
It is not possible to earn miles with BA and transfer them to QF. It is possible to use BA miles to book a QF ticket, but a transfer of miles between their programmes is not possible.
As for the credit card, I don't know since I don't live in the UK - but I think the answer is no.