Coronavirus vaccines are seen as crucial to reviving an industry that saw worldwide passenger numbers fall 75.6% last year.
Chief executive Alan Joyce said many governments were talking about vaccination as "a condition of entry".
Even if they weren't, he thought the airline should enforce its own policy.
"We have a duty of care to our passengers and to our crew, to say that everybody in that aircraft needs to be safe," Mr Joyce said.
He believes that would justify changing the terms and conditions on which tickets are booked.
And Mr Joyce thinks passengers would be willing to accept the change. "The vast majority of our customers think this is a great idea - 90% of people that we've surveyed think it should be a requirement for people to be vaccinated to travel internationally."
But some powerful voices are among those who disagree, including the World Health Organisation. Its director of digital health and innovation, Bernardo Mariano, told the BBC: "We don't approve the fact that a vaccinations passport should be a condition for travel."
He added that - regardless of what the private sector wanted - a unified approach from governments would be needed to make such a change work.