Darnell will have "clean and repair" surgery to ensure his wounds do not become infected. He may also have to have plastic surgery "down the line", Minarapa said.
She said Darnell was in high spirits, despite the attack.
"He is talking and he is doing really good. He is asking for family members and telling us what movie he wants to watch, and things like that."
Minarapa said Darnell had asked to watch the movie Garfield while he waited but said she would be "a lot more relaxed once he gets out of surgery".
Emergency services were called to the Takanini home at 1.22pm. A hospital spokeswoman said it was understood the boy had a "significant facial wound".
Caesar's owner, Henare Carroll, said he was shocked the dog was so violent as it had been brought up around people.
Carroll said his nephew was staying at his home on Matawalu Place for the weekend and his mother had just dropped him off when the incident occurred.
Though he didn't see the attack happen, he said he believed Darnell had run to play PlayStation with Carroll's friend and had jumped from the couch on to a bed in the garage - which doubles as a sleep out - giving Caesar a fright.
Caesar attacked the boy, pinning him to the bed and mauling him.
Carroll and his partner ran into the garage, and Caesar ran away and hid, he said.
"Darnell sat up and said 'I'm ok, I'm ok' but when I saw his face, I knew he wasn't ok," he said.
Blood stains are visible on the floor in the garage where the attack took place.
Carroll said he was shocked by the attack.
"Caesar was brought up around people. I thought he was a good dog. He would only attack if he was provoked."
He had surrendered Caesar to animal control, and expected he would be euthanised.
Auckland Council manager of animal management Geoff Keber said the dog was taken to a shelter.
The animal management team had taken statements from the parties involved, and their investigation was ongoing.
A study published in August found 99,000 dog bites had been recorded nationally in the decade to 2014 - with more than 5800 requiring hospital treatment. Incident rates increased from 10.5 attacks per 100,000 people to 14.3 over the 10-year period.
More than 2500 charges were made under the Dog Control Act in the past five financial years. Just over 350 dog destruction orders were granted in that time.
The Government's being told to take another look at the dog laws.
The dog pinned the boy to a bed at a house in South Auckland yesterday, and inflicted several facial wounds.
He says it's costing taxpayers tens of thousand of dollars, and children are being maimed and damaged for the rest of their lives.
He's wondering when enough will be enough.
