"Our planes are continuing to fly. We are running a normal operation," company spokesman Thomas Jachnow told news agency AFP, adding that two of the three planes were currently in the air.
Earlier Thursday, Air France and Emirates also announced they planned to keep their jets flying.
The Qantas double-decker plane carrying 433 passengers and 26 crew developed engine trouble just six minutes into a flight from Singapore to Sydney, and dumped fuel over Indonesia before returning to Singapore's Changi Airport.
There were no injuries to passengers or crew, officials said.
Metal debris including a part bearing the airline's red-and-white "flying kangaroo" emblem slammed into industrial and residential areas of the Indonesian city of Batam, opposite Singapore.