It is the Chairman's Lounge, although even Qantas themselves occasionally call it the Chairman's Club. It is by invitation only.
Qantas don't publish the criteria for who gets the invites. I believe the following positions consistently get invites. Senior state politicians (in cabinet/ministry also their shadows). Also it seems that if they were in cabinet/ministry, but are now outside of cabinet/ministry they still keep their CL membership as long as they were re-elected. All elected federal MPs/Senators. Mayors and Lord Mayors of large cities. Also it seems the spouses/partners of the preceding also get membership. If they are not re-elected in most cases they will drop down to platinum once their CL membership has expired, although on a case by case basis some seem to retain it once they have left office.
At least some foreign diplomats based in Australia are members of the CL, for example I know the British High Commissioner is given membership. I would suspect other ambassadors/HCs of other countries would get similar, in particular those of countries that Qantas flys to. I also expect that some Australian HCs and ambassadors overseas would be given membership. A few senior academics get membership (I know of one university professor and one chancellor who have membership). There are some senior public servants. There have been reports of union leaders being given access.
And then you have business leaders typically ones who have a big spend with Qantas.
adds more characters to meet posting requirement 
