Premier Gladys Berejiklian said people who test positive to the strains while in quarantine "will have to start the 14 days from the onset of symptoms".
She wrote about it on her blog in 2016, but it feels very 2020.
The New York governor accused the Trump administration of being "grossly negligent" by not barring UK flights as several European nations have already done.
States and territories have moved fast to update border bans, ruining many people's Christmas travel plans.
Quarantine-free flights between Australia and New Zealand could begin in early 2021.
Qantas boss Alan Joyce said a coronavirus jab will be a "necessity” to fly overseas.
This is the first time people can travel freely between the states without needing to quarantine since border restrictions were put in place in July.