Australia on Friday reported its first community transmission of the new Omicron coronavirus variant, but authorities held steady on a plan to reopen the economy amid hopes it would prove to be milder than previous strains.

The new case, a school student from Sydney, was the first confirmed Omicron infection of a person who had not travelled overseas, a sign the variant was now in the community, authorities in New South Wales state said.

"Transmission is always a concern but we again need to keep it in perspective," NSW Health Minister Brad Hazzard told reporters, explaining why Australia's most populous state was not reversing its staged reopening from strict lockdowns imposed in July due to the Delta variant.

"Worldwide there is no clarity around whether this particular variant is going to cause us anywhere near the problems that the earlier variants caused us."

Australia now has nine confirmed cases of the Omicron variant, eight in NSW, where a third of the country's 25 million people live. Although some states have tightened domestic border controls, the federal government is hoping to avoid a return to stop-start lockdowns.

Even so, it has postponed by two weeks a plan to let foreign students and skilled migrants into the country, and Australians returning from southern Africa must complete two weeks of hotel quarantine.

Asked if the federal government would stop targeting arrivals from southern Africa, now that the new variant was no longer limited to people who had been there, Federal Health Minister Greg Hunt said "we will continue to review the medical advice, but we follow it because it has kept Australia safe."

Chief Medical Officer Paul Kelly, the government's top health adviser, said Australia would not recommend bringing forward vaccine booster shots, as other countries have done, as there was "no evidence" this would improve protection against Omicron.

Australia's aggressive COVID-19 response has helped it avoid the high numbers of COVID-19 deaths recorded in many other countries, with about 212,000 cases and 2,000 deaths.

The country's remote Northern Territory, which is home to most of its indigenous population, recorded its first COVID-19 death, an indigenous woman in her 70s.