Bella-Rae Birch was mauled at her home in St Helens, Merseyside, yesterday afternoon. The little girl was rushed to hospital but died as a result of her injuries.
The dog was handed over to police and put down.
Tests will be carried out to determine whether the animal was a legal breed under the Dangerous Dogs Act.
Police remain at the scene and a cordon is in place as officers continue enquiries.
Detective Inspector Lisa Milligan of Merseyside Police said: “This is a tragic incident and our thoughts are with the child’s family at this devastating time.
“The little girl’s parents and wider family are absolutely devastated and our specialist Family Liaison Officers are providing them with support at this horrendous time.
“Whilst we are in the very early stages of the investigation into this extremely tragic incident we can confirm that the dog was only bought by the family a week ago and officers are working to identify the previous owners of the dog concerned and establish its history.
“Our officers will remain on Bidston Avenue this evening and in the coming days to provide reassurance to the local community and we will work tirelessly to establish the full circumstances.
“If you were in the Bidston Avenue area this afternoon and witnessed anything, or have any information about the dog in question then please come forward speak to one of our officers.
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The neighbour, who is due to go to university to train as a paramedic, said the child’s parents were “hysterical”.
She added: “I didn’t see the dog, I was just focusing on helping the baby.”
Another neighbour who helped to give CPR said: “The parents doted on the children. It’s too upsetting to say anything else.”
Neighbour Joanne Matthews, 53, said: “She was such a beautiful little girl, toddling about.
“I’d see the family in passing, just to say hello, and they were always very pleasant.”
Ms Matthews said she had seen the ambulance outside the house on Bidston Avenue at about 3.50pm on Monday and then about 10 police cars, including a van, arrive.
Anyone with information can contact Merseyside Police on Twitter @MerPolCC, or Merseyside Police Contact Centre on Facebook, with reference number 22000196837.
They can also contact Crimestoppers anonymously on 0800 555 111.