West Australian Premier Mark McGowan expects the take-up of the coronavirus vaccine by frontline workers to accelerate quickly after a slow start to the rollout.
About 800 doses of the Pfizer vaccine have been administered by WA Health so far, with that number expected to reach 1000 by the end of Wednesday.
That does not include people in aged and disability care whose inoculations are being handled by the federal government.
More than 3200 people received jabs during the first two days of the rollout in NSW.
"It was always going to have a reasonably slow start but I think it will pick up very quickly and we'll see major take-up of vaccinations across Western Australia over time," Mr McGowan told reporters on Wednesday.
"Obviously there's limited supplies initially so we're getting as many people vaccinated as quickly as possible and over time that will increase as more supplies come to hand."
WA Health is managing the rollout of the vaccine to hotel quarantine workers and staff at Fremantle Port and Perth Airport.
The state will receive about 5000 doses of the Pfizer vaccine each week for the first three weeks, with about 3900 reserved for WA Health.
Mr McGowan said he was concerned by news that two elderly aged care residents in Queensland had been given four times the correct dose of the vaccine.
The jabs are supervised by two nurses under WA Health protocols but these do not apply to people in aged care who are under the federal government's responsibility.
"Obviously what's occurred in Queensland appears to be a big mistake," the premier said.
"I'd urge the Commonwealth government to get onto it and make sure they have the highest standards in place into the future to keep public confidence in this program."