A source close to the child said the injuries had left many in the community "overcome with emotion".
It is understood the girl is one of six children. She and her siblings were put into Child, Youth and Family care before she was admitted to hospital.
The source said her parents were at her bedside in hospital. They were not with her when she was injured.
The girl's mother has been posting on Facebook about her child. She said her family did not believe a story they had been told about the girl being injured as a result of falling off a bed.
Her daughter was "in pain" but doing "extremely well".
The child's step-grandfather had also written about the ordeal on Facebook. He said the girl had been living with him until CYF stepped in.
"My baby ... is in ICU in a coma, she is only 12 months and 10 days old, apparently she fell off the bed and now she is in a coma," he said.
"She was taken from my care on the 20th of July into [CYF] care. I had only seen her once since for one hour. Now she's in a coma and I'm hurting big time.
"Don't leave me, my baby. Daddy Pop loves you and I want you to come back to me please my darling."
A CYF spokeswoman said the agency would not comment while the matter was under police investigation.
She would not clarify if the girl was in CYF care at the time she was injured, or if the agency was involved with the family.
"This is a matter for police," she said. "As is usual, we are working with police and the family around the safety and ongoing needs of the child."
