The ramped up security procedures were put in place after four men were arrested at the weekend in raids conducted across several Sydney suburbs.
Local media said the plot may have involved a bomb or poisonous gas.
Friends Georgie and Brianna said they had arrived early because of the heightened security measures but were told they would have to wait to check in.
Police at the Surry Hills address where two of the men were arrested. Pictures showed forensic-specialist officers wearing masks and plastic jumpsuits inside the properties and combing through rubbish bins outside.
Extra security measures now being deployed at Australian airports, described by the Prime Minister as "very robust" and he is thanking the travellers for their patience.
"The enhanced and upgraded security measures have been implemented in full at Canberra Airport and there are minimal delays to the public", the spokeswoman said.
Security at Brisbane Airport was visibly beefed up on Sunday, with travellers asked to arrive early and pack light.
Passengers at major Australian airports, including Sydney, experienced longer-than-usual queues during the busy Monday morning travel period.
But Sydney Airport's plan takes that further, linking the same facial recognition system with every other touchpoint throughout the terminal, including baggage drop, admission to the security screening queues, clearing passport control without a passport, completing duty-free purchases and even entering airline lounges document-free.
Inter-state travellers are subjected to far less scrutiny than those travelling overseas with no formal identification checks required for domestic trips.
"Travellers should be prepared for additional scrutiny at screening points, and while it is important that Australians are aware of the increased threat, be assured we have the finest security and intelligence services in the world and they are working, as is my government, and all our governments around Australia, night and day to keep Australians safe", he said.
Australia has been on heightened alert since 2014 for attacks by home-grown militants returning from fighting in the Middle East, or their supporters, but has suffered few domestic attacks.
Australian police have alleged that a group of Sydney men were planning to use an "improvised device" to target the aviation industry however no details on a target, location, date or time have been uncovered. The offences are not related to the alleged plane bomb plot.