The first TAA A300 arrived in middle of 1981. It was two class configuration - I think it started off as 40/229. The first Ansett 767 arrived two years later. Business Class arrived after the first planes.
The first four A330s arrived fairly quickly, but the fifth plane was delayed. TAA had ideas of leasing it out to Air Pacific, but Air Pacific decided to carry on buying seats on Qantas planes. (Air Pacific had a short lease of a DC-10, but that is another story).
Just after the Qantas Australian Airlines merger, Airbus had some spare A300s which had been used by Philippine Airlines. These aircraft were offered to Qantas (new management, who had arrived from Australian Airlines) and Airbus found they were half interested. This might have added another four planes to the Qantas fleet.