Recent travellers to South Australia from NSW and Queensland will be messaged to check on any exposure to new COVID-19 cases in those states.

Text messages will be sent out asking people to complete a short survey to check if they have been to any places of risk.

But no other restrictions are being put in place at this stage.

Chief Public Health Officer Nicola Spurrier says while there are new infections, they were picked up quickly.

"We have very good information about where the people have been," she said.

"They have really good contact tracing and all of the information has been shared with us.

"I'm quite happy with the situation at the moment."

In Queensland, a doctor at a Brisbane hospital tested positive, while in NSW a worker at a quarantine hotel has also become infected.

Also on Monday, Professor Spurrier, Premier Steven Marshall and Health Minister Steven Wade received their second dose of the Pfizer vaccine.

Mr Marshall said SA delivered about 8000 doses in the first three weeks, short of its initial target of 12,000.

But the premier said he made no apologies for taking a steady approach.

"We said from day one we want to get this right, not rushed," he said.

On the flip side, Mr Marshall said the government was very happy with the spread of the vaccine across the state, with clinics set up in a number of regional and remote areas.