Police have established a task force to investigate the death of Charlie, who was found to be unresponsive at a home in suburban Munno Para on Friday.
She died soon after arrival at hospital.
Her death has been declared a major crime and is being treated as a case of criminal neglect.
Police said five other children aged eight, 10, 13, 14 and 15 were also removed from the home amid varying levels of concern for their wellbeing.
Deputy Police Commissioner Linda Williams said a range of government agencies had interacted with the family and the extent of those interactions would form part of the investigation.
She said police would allocate all the necessary resources to determine what happened and whether any charges could be laid.
Interim post-mortem results raised concerns about the state of Charlie's health and wellbeing at the time of her death.
"We want to understand what happened to Charlie and how she ended up in the circumstances that she did," Ms Williams said.
"The death of any person is tragic, but the death of a young child, a six-year-old girl, obviously causes concern for everybody to want to know how this occurred."
The deputy commissioner said conditions in the home were described as poor, but she was unable to elaborate.
She declined to comment in detail on who police were speaking to and the level of co-operation they were receiving.
Acting Premier Susan Close said that as an immediate response to the case, the government had ordered a review of the interactions between state agencies and the family over the past couple of years.
"The review will encompass the chronology of the services delivered and the agencies engaged," Ms Close said.
"It's important not to pre-judge what that review will find.
"What we need to do is go through the process and ask what interactions occurred, could they have been any different and are there any lessons."
Charlie's death will also be subject to a coronial inquiry.
Child Protection Minister Katrine Hildyard described the girl's death as heartbreaking and said her thoughts were with her family and friends.
"What I can say is the family were known to multiple government agencies who were actively involved with them over the past couple of years," Ms Hildyard said.
"All government agencies that had contact with this family will, of course, fully co-operate with the inquiries that follow this tragedy."
Those agencies included the Child Protection Department, Human Services, Education and Housing.
Ms Hildyard said child protection was an incredibly complex system, but one that "had to do better".
"I and our government will be relentless in our efforts to improve the system," she said.
"I do understand that people are frustrated."
