It is not yet known the exact circumstances of events in the lead-up to the attack on the girl.
However, it is believed the dog was a Rottweiler belonging to her father which has since been humanely destroyed.
The attack happened shortly after 2 pm on Sunday at the family home, which is in the Garvagh area.
Ambulance Service staff administered first aid before she was airlifted to the Royal Belfast Hospital for Sick Children by the air ambulance.
Local DUP councillor Adrian McQuillan, who knows the family, said the whole community is in a state of shock.
He told the Belfast Telegraph: “My heartfelt sympathy goes out to this family who must be in so much turmoil right now.
“They are in the midst of what is undoubtedly a nightmare for any parents and I know the whole community is thinking and praying for them right now. I understand this poor wee girl, who is only three years of age, has been badly mauled in her face by the dog which is owned by the family. Initial fears that she would lose her eye as a result of the attack don’t seem to be the case now, which is a mercy,” the councillor added.
“Sadly this family face a long time of uncertainty, of long vigils at their daughter’s hospital bedside, but I do know whatever support they need to make this terribly traumatic time a bit easier they will get from the local community.”
A Causeway Coast and Glens Council spokeswoman said: “Council is aware of an incident on Sunday, April 26 involving a young child and a family pet which resulted in hospital admission of the child.
“As a result, the family has had the animal humanely destroyed.
“Council sends its best wishes to the child and family and hopes that a full and speedy recovery can be made following such a traumatic experience.”
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