Nicola Keane, who worked at Children's Health Ireland in Crumlin, fell to her death after jumping from the M50 toll bridge at 3.45am yesterday.
The body of her seven-month-old son Henry was found by gardaí at the family home in Shackleton Way, Lucan, around an hour later.
The infant was found in an upstairs room, and his death was last night still officially classified as "unexplained" by gardaí.
A post-mortem carried out at the same hospital where his mother worked revealed he had died from asphyxiation.
Senior sources said the results "have not conclusively determined" if the child was the victim of homicide and have not led to a definite line of enquiry.
It is understood Ms Keane had been suffering from post-natal depression in recent months.
Ms Keane was originally from Ballina, Co Mayo, and her death and that of her baby caused shock in the town.
"The whole town is devastated, everyone is distraught," Fianna Fáil councillor Annie May Reape said.
"They were the most beautiful people and are thought of so highly by everyone.
"Her mother, Mary, was the most fabulous community-spirited woman and they raised fabulous, kind girls.
"This is the worst of tragedies. We're praying for them."
A garda spokesman said: "The primary focus of the investigation team at this time is the preparation of an investigation file for the coroner in respect of the still unexplained death of the infant boy."
Gardaí saw no signs of violence or any obvious evidence of a violent death when they carried out a forensic examination of the property in which the dead child was found at around 5am yesterday.
The body of Ms Keane was discovefred at Lower Road, Strawberry Beds, after she jumped from the M50 toll bridge at around 3.45am.
She had been seen behaving erratically on the bridge after driving to it and getting out of her car.
Gardaí found the car was registered to an address at Shackleton Way in nearby Lucan.
It is understood that when they called to the property, Ms Keane's husband was asleep.
He had been unaware the child was dead.
There were no other children in the house.
A post-mortem on Ms Keane's body is due to take place today at Dublin City Morgue.
Gardaí said they are not looking for anyone else in relation to the tragedy.
Officers continued to examine the Shackleton Way property while detectives carried out door-to-door enquiries.
There was a deep sense of shock in the neighbourhood, where only days before her death Ms Keane had been seen walking her baby son.
"I talked to her a few times. She was really friendly and seemed happy. Her little boy was beautiful," a female neighbour said.
"We always saw the couple walking up and down with the baby in the pram. They're a lovely couple.
"We're shocked. They walked up and down every day and she looked like she was in good form.
"This is the last thing we would have expected. I saw her a couple of days ago just walking the baby up and down.
"Everybody is doing that now. Walking their babies round the estate. This is a family neighbourhood."
Another neighbour said: "This is a happy family. This doesn't happen. They were happy, you could see it.
"This is just shocking. I can't take it in. I can't stop thinking about the baby, he was just seven-months-old."