The fire started just before 5am in a bedroom on the second level of the two-storey home in Islington Crescent.
One of the occupants woke up to the fire in their bedroom and had enough time to pick up the baby, who was sleeping close to the flames, and flee.
Four other people also made it out of the house.
The baby was assessed by NSW Ambulance paramedics for smoke inhalation and transported to hospital, as a precaution.
The cause of the fire is not being treated as suspicious.
FRNSW Superintendent Adam Dewberry said the bedroom was not fitted with a smoke alarm.
“We are very fortunate the father woke up before the fire took hold,” Supt Dewberry said.
“People can not smell smoke when they are asleep, so it’s crucial to have working smoke alarms in your home.
“The law requires a smoke alarm to be fitted to each level of your home.
“FRNSW also encourages people to fit alarms in bedrooms, especially if you sleep with the door shut.”
