Ayen Chol died at the scene after the dog entered the home where she was playing with her five-year-old cousin on Wednesday evening, police said.
Another cousin fought to fend off the vicious animal, suffering bites to her arms and hands during the struggle, during which she tried to beat the dog away with a table, local reports said. The five-year-old was bitten on the face.
Both were rushed to hospital in a stable condition.
“It’s yet to be fully investigated to see whether or not there’s been any offence committed,” said Superintendent Graham Kent.
“Our focus at this stage is to find out what happened and in the process of doing that we will find out whether or not there’s been any offence.”
The dog, which belonged to a neighbour, is expected to be put down.
The family, which arrived in Australia in 2004, were being comforted by the local Sudanese community.