SA Health has confirmed the child's mother, who also tested positive for the virus, has travelled with the teenager as a support person.

Both cases have been counted in the NSW tally but come as SA officials continue to express concern over infections so close to the state's borders.

South Australia on Tuesday reported another case of the virus in a returned overseas traveller, a man in his 30s, who has been in hotel quarantine since his arrival.

His infection is considered to be old but has been added to SA's total because it was not previously diagnosed.

Also on Tuesday, SA Health confirmed a surge in COVID-19 vaccination bookings after tweaking its program, making the Pfizer jab more widely available.

SA Health said 35,000 bookings were made on Monday, the first day people aged over 60 became eligible for the Pfizer dose.

About 11,000 of those bookings were made for younger children aged 12 to 16, who can also attend clinics on a walk-in basis.

The rise in bookings came as Deputy Chief Public Health Officer Emily Kirkpatrick defended SA's continued tough stance on arrivals from NSW and Victoria, particularly among locals seeking to return or those applying for exemptions.

While staff considering those exemptions were currently dealing with about 7000 applications, Dr Kirkpatrick said it was important each one was considered on its own merits.

"They do all still need to be considered on a case-by-case basis," she said.

"We're at the point where there is so much risk in NSW and Victoria, we absolutely need an individual lens on these applications."

Health Minister Stephen Wade said the heartache being experienced by those people waiting to return or waiting for exemptions was clear, but would be worse if there was a major outbreak of the Delta strain of the virus in SA.

"It's completely understandable that people are distressed as they wait for consideration of their application," Mr Wade said.

"It's very important that we make sure each of those applications is properly considered because every single case could represent the introduction of Delta to our state.

"The heartbreak that would be caused to our state if there was an outbreak in South Australia like there has been to the east is something this government is very determined to avoid."

SA is currently dealing with 10 virus cases acquired either interstate or overseas, including a miner who flew into Adelaide from Sydney last week.

His infection forced about 45 people into isolation including some on the same flight.

They have all tested negative so far.

Altogether SA has about 600 people in quarantine, including people who may have come in contact with a number of interstate truck drivers who tested positive for the virus after travelling into the state.

SA Health said so far 98 per cent of those people had also tested negative.

Australian Associated Press