Qantas said it is considering a plan to reward customers who have received both doses of a COVID-19 vaccine.
The airline has said it will require all passengers to be vaccinated when it restarts international flights beyond the New Zealand bubble.
The policy has been criticised by the World Travel and Tourism Council, which has labeled it as discriminatory.
"As a large company that relies on travel to put our people and planes back to work, we're obviously motivated to help with the national vaccine effort," Tully said in a statement.
"We're still thinking through how this would work, but the incentive could be Qantas points, Qantas or Jetstar flight vouchers, or status credits for frequent flyers."
Domestic travel increases
The new routes include Townsville to Adelaide/Melbourne/Sydney, Adelaide to Cairns/Hobart, Sydney-Uluru and Perth-Gold Coast.
This brings the total number of routes Qantas and Jetstar have added since the start of the pandemic to 45.
Flyers will also see more widebody aircraft with Business Suites on flights between the east coast capital cities into Perth and Darwin.
Usually used for long haul international flights including Perth-London, the 236-seat Boeing 787-9 Dreamliner will begin operating up to nine Sydney to Perth flights per week.
Qantas domestic and international CEO Andrew David said the new routes would support the growing demand for domestic tourism.
“As most international travel remains off limits for now, Australians are taking more regular holidays within the country and we expect these new direct flights to key tourism destinations will be popular with travellers,” David said.
“Our strategy of adding new domestic routes is generating revenue from our aircraft rather than leaving them on the ground. It means more work for our people and even more low fares for our customers.”