The question doesn't specify 'continuous operation'. Therefore the the correct answer is FALSE.
KLM: october 7, 1919Still in operationOperations stopped during World War II (in Europe) apart from the operations in the Dutch Antilles in the Caribbean. Merged with Air France in 2004. The airline is the "Oldest operating airline by date".
QANTAS: November 16, 1920Still in operationHolds title of "Second oldest operating Airline by Years in service" After KLM. As well as "Oldest Continuously Operating Airline in the World." Due to KLM suspending service during WW2.
The Queensland and Northern Territory Aerial Services was started in Queensland by Paul McGuinessy, Hudson Fysh, Fergus McMaster and Arthur Baird in 1920. It was originally used for delivery mail and by the Royal Flying Doctors service of Australia.