South Australians are currently required to self-quarantine on arrival in WA but will be free to travel without taking a COVID-19 test from Friday.
Mr McGowan has also raised concerns over a mutation of the virus currently running rampant in the United Kingdom.
“I raised that at the [state] emergency [management committee] meeting this morning because some countries seem to be shutting down flights from Britain,” Mr McGowan said.
“The Commonwealth government seems not to be doing that.”
More than 40 countries have banned UK travellers as detections of a variant of the virus – which the country’s Prime Minister Boris Johnston said could be 70 per cent more transmissible – are on the rise.
There were 33,364 new cases of the virus in the UK on Monday with more than 200,000 positive test results in the past week.
Canada, Russia, Switzerland, Spain, France and Germany are among the nations to close off travel to the UK or signal border controls in the coming days.
Australia has so far ruled out any bans on UK flights coming into the country, with Chief Health Officer Paul Kelly saying on Monday there was no definite evidence the strain was a significant change.
“There has been more transmission in recent in times in south east of UK and that’s maybe associated with the virus. There is certainly more transmission going on but that is also related to the few weeks before Christmas,” he said.
“There are three things going on, an environment, a host … and the infectious agent.
“The infectious agent has changed a little, there are a lot of people moving around in south-east England … it’s also winter, so those all three are important elements to consider.”
Dr Kelly said everyone from the UK still had to go through 14 days of quarantine on arrival in Australia and the hotel isolation system had been mostly effective.
Mr McGowan said he had faith in WA’s quarantine system.
“We’re only as good as our weakest link which is why we constantly monitor and review our systems,” he said.
“I’m desperate for us not to get any new cases.”
Peter de Kruijff is a journalist with WAtoday.