Well...

I learnt that QANTAS issues Temporary Cards in SOME lounges, but then may (are) not recognized by other Airlines, according to QF Reps.

QF does not send a fax or any document with their logo (at least I didn't get) and tried with LAX and Australia.

Australians get their Permanent Card in 10 to 14 days: Now if anyone enrolled under any Australian Corp Agreement QF will be sending the cards & Kits (in that amount of time) to the person responsible for the Corp.Agreement who then is to send it to you. You should arrange with this person to have the Card&kit couried to you.

Last but not least, QANTAS LAX seemed highly professional and willing to help within their boundaries, which (on the phone) seemed to be :
a) If in LAX, you're invited to QF Lounge, by informing your FF number ;
b) At all times the QF system already shows you're a member ;
c) Elsewhere, if an AC Rep is willing to call QF Toll-Free number 1.800.227-5400 upon informing your QF FF number they'll confirm whether you're a Club member or not;
d) No way are they allowed to print or create a document.

QF sends emergency cards by courier, (AUD30,00) but then I received conflicting information whether that would be any faster than the regular amount of time.

My e-mail to QF was replied in approx 24 hours.

Hope it has helped you, instead of bringing more confusion... And if anyone has found different information please share.