Ms Organ said she believed the neighbour was minding her grandson for the weekend.
The Welsh Ambulance Service NHS Trust said it received a 999 call from Gwent Police to attend the house at 0021 GMT.
"The call said a young child had been attacked by a dog," said a spokesman.
"We arrived shortly afterwards and conveyed the child to the Prince Charles Hospital in Merthyr."
The spokesman added that a second patient was taken to the University Hospital of Wales in Cardiff for treatment shortly after 0200.
Chief Inspector Jim Baker said: "This is a tragic incident for the family and the community.
"Gwent Police family liaison officers are currently supporting and assisting the family through this difficult time.
"The family wish to be left alone to grieve.
"Although the exact circumstances of the baby's death are yet to be established, we would like to reiterate the advice given to dog owners that dogs should never be left unsupervised with young children at any time."
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