Well, welcome to the OneWorld side of the flying world. QF will not comp your status but getting status with QF when traveling premium cabin is not that hard.
You should chose carefully which FF program you would like to join. It usually comes down to a AA vs QF discussion and there are many threads in the OW forum about that.
Summary: AA has a much better earn/burn ration and much lower fees than QF. QF however offers you the advantage of greater award availability for their own status people, much better lounge access (especially as a QF WP) and the other advantages you get when belonging to the FFP of the airline you actually fly with.

Regarding credit card: Many banks have credit cards which give you QF points. Or American Express which has a decent rewards program which includes points transfer to QF.