Both are understood to have lived at the address in Enderley where the attack happened about 7pm.
Dog Control Hearing Panel chairman, councillor Ewan Wilson, said the rottweiler was registered but the other dog was not. He did not know why.
"We were asked to respond on behalf of police. The animal is being held until the police complete their investigation.
"If the investigation leads to charges we will continue to keep the animal secure until the decision of the court.
"If the court then orders the dog destroyed, then the dog will be destroyed."
Wilson said if police did not lay charges the owner could surrender the dog to the council for destruction.
But even if the police did not lay charges, the council would not give the dog back to its owner, he said.
The council would then conduct its own investigation under the Animal Control Act.
"If we chose to prosecute then we would go directly to the District Court for a destruction order of the dog."
The subject of any council investigation would be the registered owner as well as whoever was in control of the dog at the time of the attack.
Wilson said he did not know who the registered owner of the dog was. He said the situation could potentially be drawn out over many months.
The mother of the newborn said on social media she wished she could turn back time.
She posted a poignant message online yesterday acknowledging her devastating loss and the events of the past few days.
Sharing a photo of herself relaxing outside on a sunny day, sitting on the grass and looking towards a river, she shared the words:
"If only I could go back to this day with [you] still in my tummy, my son."
Friends and family offered their condolences and support to the woman.
One wrote: "I have no words, my friend. We are all trying to carry your loss for you, but I guess you won't even feel it as the weight is so heavy.
"We love you ... and we got you. Hang in there and breathe."
The young mum also shared a photo of her little boy who appears asleep with his hands up near his cheeks in small fists.
Neighbours who rushed to help the mother and her baby described upsetting scenes. One woman told Stuff it appeared the animal had tried to bury the infant after attacking him.
Brothers Takilesi and Junior Afamasaga told Newshub they ran over after hearing the woman's screams for help - and were confronted with the tragedy.
"[She] was just trying to keep the baby awake, trying to keep it crying.
"She asked me for a cloth - so I took off my hoodie and gave it straight to her," one of the brothers said.
It is understood the mum was in the toilet when the attack happened.
The child's death has been referred to a coroner.
Animal behaviourist Mark Vette told NewstalkZB dogs did not naturally learn who their extended family was - they needed to be taught and exposed to them during the early stages.
That was particularly important when introducing a baby or children, for example, over a matter of a few months.
"Don't leave your baby alone in the early stages, at all.
"When the baby comes into the house, it's a new being. It behaves very differently from adults. It can be very unusual and a bit frightening or threatening to hear baby crying - for the dog," he said.
"So that assessment should be made very early on - that your dog is really safe around your baby."
- Additional reporting: Nikki Preston
