Firefighters rescued Libby-Jayne Hornsby from a blaze at her home in Don Street, Conisbrough, near Doncaster, at about 8pm on Thursday night, but she later died in hospital.
Her mother, Kelly Hambrey, said the toddler was loved by all in her extended family.
“Libby-Jayne was a perfect little girl, always smiling and happy,” she said.
“She was our world. As a family we want to thank our friends and neighbours for their support at this time.”
Father Neil Hornsby said her daughter was always full of life, with “bright hair and bright eyes”.
“Before Libby was born I felt something was missing in my life and after she was born I knew that I had found what was missing - it was Libby,” he said.
“My life with Libby was brilliant, but now there is something missing again.”
Mr Hornsby said he wanted to thank the emergency service crews who did all they could to save his little girl.
The couple have asked for privacy while they grieve.
The cause of the fire remains under investigation, but investigators have determined it involved bedding in the main bedroom on the property’s first floor.
Authorities had earlier said there were no working fire alarms in the property, and said the case was a sombre reminder for people to have them installed.
A neighbour initially alerted emergency services to the incident.
Two fire crews were called to the blaze.