A child under 12 months of age could not be transported to John Hunter Children's Hospital in the state's Hunter Valley after suffering an anaphylactic reaction at home this week.

The child's mother was able to administer an EpiPen before being advised by NSW Ambulance they could not provide transportation from a Lake Macquarie suburb to the hospital due to a lack of available vehicles.

In a statement to the Newcastle Herald, an Ambulance NSW spokesperson said the service was facing "unprecedented demand" as a result of the pandemic, with control centres fielding 4000 triple zero calls most days so far in January.

The spokesperson said an intensive care paramedic in a rapid response vehicle, which cannot transport patients, was sent to the scene within a few minutes of the triple zero call. After the child had been assessed, the paramedic followed the mother to the hospital. The mother was advised by NSW Ambulance to pull over if the child deteriorated during the drive to hospital.

A doctor who works at the hospital - but does not have permission to speak to media - said there were a "number of dangers" associated with a parent driving a child to hospital in high-stress situations.

"Before this happened, another child and family were brought in, all critically injured, because they had tried to drive the child - who was also under 12 months of age - to hospital. And in doing so, they had a serious car accident," the doctor said.

"Now their major illness is actually the injury caused by the car accident.

"We have seen the possible consequences of parents needing, in high stress situations, to drive their children to hospital."

The doctor suspected the ambulance service was experiencing staff shortages, as well as an increase in call outs, due to COVID-19.

But he was concerned the flow-on effect could mean a critically ill child died because they could not get an ambulance quickly enough in an emergency.

"This was a near miss," he said.

"This was a mother who was equipped in that she had the EpiPen, and she was confident and competent in a time of high stress, and obviously, that is not going to be the case for a majority of parents. My fear is that a critically ill child will die as a result of not being able to be transported to hospital because of the stress on the system due to COVID.

"You can only imagine what it would be like to be told to put your baby into your car yourself because no ambulance is going to arrive in time to take them to hospital."

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The doctor said parents should feel comfortable calling an ambulance or seeking care for their children at hospital, even during a pandemic.

"It is not their job to work out if they need an ambulance or not, and it is not their job to know whether they need to come into hospital and be seen or not," he said.

"Obviously, because of the pressure on the system there are prolonged wait times and there are more stressful elements associated with coming to hospital now in that we can only allow one parent or guardian to be with a child at a time.

"For adults, no visitors are allowed.

"So if they can be as patient as possible with staff with the wait times, and understand there is reduced visitor access, that would be very much appreciated.

"It seems to be occurring every day where staff members, particularly the nurse and admin staff at the front, are at the very least being verbally abused by people who are unsatisfied with the wait time or the inability to bring extra family members in."

The Ambulance NSW spokesperson said that in response to the increased demand, the service had "surged" all operational staff and recruited an extra 50 call takers.

Ambulance NSW is inducting 60 graduate paramedics, with another 200 to begin induction in the coming weeks, and 65 casual paramedics had been offered full-time employment, the spokesperson said.