Staff at Royal Hobart Hospital have successfully stabilised a newborn baby boy after he was miraculously delivered following the death of his mother in a horror car crash in Hobart yesterday.

Sarah Paino, 24, died when her car crashed with an SUV that was allegedly stolen and speeding.

Ms Paino's two-year-old son was also in the car but survived the crash, suffering only minor injuries.

The young mother was killed in the crash.

Ms Paino had a two-year-old son and was heavily pregnant at the time of the crash.

Police say the stolen SUV carrying two boys and two girls aged between 12 and 15 appeared to have run a red light when it hit the mother's sedan, killing her.

Ms Paino, who was 32 weeks pregnant, was driving home after dropping her partner off at work at a bakery when her car was hit at an intersection in central Hobart at 1am.

The baby, who was later delivered at the hospital, is a boy, the ABC reports.

The SUV came to rest on a footpath on the opposite side of the road after hitting a nearby building and bursting into flames.

Police arrested a 15-year-old boy in suburban Hobart six hours later.

The teenager is alleged to be the driver and was remanded in custody after facing a youth justice court on Friday charged with manslaughter and stealing a car.

He didn't apply for bail and will appear in court again on February 2.

Police are investigating.

Police have laid charges against the three other passengers of the SUV, who along with the alleged driver suffered minor injuries and went to hospital.

Police commander Glenn Frame described the crash as a tragedy for everyone involved but an avoidable one.

He said police will ensure Ms Paino's partner and father of their children receives appropriate support and care.

"Our deepest sympathies and condolences go out to the family and the friends of the deceased," he said.

Mr Frame said officers tried to intercept the speeding SUV twice before the crash, after seeing it driving fast with its lights off.

There were no obvious signs of braking at the crash site.

Ms Paino's baby was delivered alive.

The crash occurred in central Hobart.

But they did not pursue it as per police policy.

"When you have young, inexperienced drivers in stolen vehicles driving like idiots that puts the public at risk," he told reporters.

"The last thing we want is police vehicles pursuing those vehicles and putting the public at risk.

Police had first spotted the stolen car five minutes before the crash.

Police located a teenage boy, who they believe to be the driver of the stolen car, nearby.