by whom was the airlines set up?
The Australian National Airways Commission.
Trans Australia Airlines
The Commission decided on the name "Trans-Australia Airlines", applied to the Treasury for a preliminary advance of £10,000 and set about making plans, recruiting staff, and purchasing equipment. Reginald Ansett, proprietor of the small Victorian company Ansett Airways was quick to offer to get the new airline off to a flying start by selling his entire operation to the ANAC 
who was lester brain? He was a pioneer Australian aviator and airline executive. where was he born? Forbes, New South Wales. did he take part in any war? Yes, World War II. what role did he play in it? He coordinated his airline's support for the Australian military. which airlines was he a part of? Trans Australia Airlines (TAA). where is the museum of this organization located? Airport West Training Facility (formerly the TAA/Australian Airlines Flight Training Centre).
wiki:13608936
Trans Australia Airlines [SEP] Beginnings
He was 'a great believer in competition for business' and would not have accepted the post of Chairman of the ANAC had the monopoly provision been retained. The Commission decided on the name "Trans-Australia Airlines", applied to the Treasury for a preliminary advance of £10,000 and set about making plans, recruiting staff, and purchasing equipment. Reginald Ansett, proprietor of the small Victorian company Ansett Airways was quick to offer to get the new airline off to a flying start by selling his entire operation to the ANAC as a going concern, including (if desired) his own services as managing agent.