The duo, aged in their 30s, arrived on Sunday night on flight VA470, hours before WA's reintroduced hard border to Queensland came into effect.
WA Health on Tuesday said the pair were in self-quarantine and four of their close household contacts had tested negative. A fifth person was awaiting a test result.
Authorities have so far identified two exposure sites: 7-Eleven in Midland and the Virgin domestic terminal at Perth Airport.
Other passengers from the flight are asked to monitor for symptoms and comply with testing requirements.
The state's plan to lift travel restrictions from February 5 has been clouded by a dramatic rise in cases in NSW and Victoria.
National cabinet will meet on Wednesday to discuss the influx of Omicron infections amid calls from the Australian Medical Association to adopt a national response, including venue density limits and mandatory indoor mask-wearing.
WA's government has avoided imposing such restrictions for much of the past two years at the expense of keeping borders closed.
But AMA President Omar Khorshid believes already-strained hospitals will struggle to cope unless the nation slows the spread of Omicron.
"We expect hospitals to be under extraordinary pressure ... even if Omicron is more mild in a vaccinated population, even if we don't see huge numbers of hospitalisations," Dr Khorshid told reporters in Perth.
"The fact healthcare workers can't go to work with Omicron, they can't go to work if their child has Omicron, we expect that impact itself to really restrict our ability to deliver healthcare, to effect elective surgery, to effect our performance in dealing with emergency presentations.
"All of that, we think, should be avoided by sensible measures now."
WA's government on Tuesday played down concerns from doctors at a major regional hospital in Bunbury who had written to the health department warning about the facility's inability to cope with a major outbreak due to understaffing.
The McGowan administration has poured billions of dollars into the health system in recent months as public hospitals struggle to cope with low staffing and other performance issues.
Dr Khorshid said WA authorities would be closely watching the situation in NSW after the state on Tuesday posted a record 3057 new cases in a single 24-hour period.
"If we get to late January and we're seeing large numbers of cases but really not a lot of severe illness, then WA's border may well open the way it's been set," he said.
"But I think if we're seeing the hospital system in NSW collapsing, I would expect the premier to keep our border either shut or at least very heavily restricted."
WA's border reopening is expected to align with the state's double-dose vaccination rate for residents aged 12 and over reaching 90 per cent.
The state reached that threshold over the weekend for first doses.
A low take-up in the regions remains a significant concern and will almost certainly prompt the introduction of localised restrictions for unvaccinated people in those areas.
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