Eliza-Mae Mullane, from Pontyberem, Carmarthenshire, was flown to hospital in Cardiff but could not be saved following the attack in February.
A coroner said she suffered a serious head injury and ruled her death was accidental.
Her father wanted the potential danger of family dogs highlighted.
Eliza-Mae's mother Sharon John left her sleeping daughter in her pram in the living room while she put her son in a taxi for school, the hearing was told.
When she returned she found one of the family's pets had pushed its way into the room and Eliza-Mae was on the floor.
A post-mortem examination found she had died from head injuries with internal bleeding.
Coroner Mark Layton said: "Eliza's mother could not have possibly foreseen this happening."
An Alaskan Malamute dog owned by the family was put down, along with their other dog a collie-cross breed.
The hearing was told the dogs had never shown any signs of aggression.
A statement from Eliza-Mae's father Patrick Mullane said: "I hope Sharon, the children and I can move on from this sadness and recall with joy the short time we spent with Eliza-Mae.
"I hope this inquest will raise public awareness of the potential dangers family dogs can present to very young children."
Following the tragedy, Eliza-Mae's parents said they would cherish the short time they had with her.
Officers were called to baby girl's home on the morning of 18 February.
Police sealed off the house and the ambulance service was called to the scene.
Eliza-Mae was flown to the University Hospital of Wales in Cardiff where doctors pronounced her dead.
A six-day-old baby girl died after being pulled from her pram and bitten by the family's pet dog at her home, an inquest has heard.