The boy was badly mauled by the family pet on Sunday afternoon and later died in hospital from his injuries.
Both parents, a 35-year-old man and a 27-year-old woman, have been arrested on suspicion of gross negligence manslaughter, but have now been released on bail pending further enquiries.
A spokesperson for South Yorkshire Police declined to give any more details about the dog, including whether the force had chosen to put it down, except to add it was a crossbreed.
One neighbour, who said she was driving past when the police arrived, wrote on Facebook: “The dog was a big fluffy golden dog, it looked harmless at first glance.
“I couldn’t tell you the breed but three police officers were struggling to control it to get it into the dog van.
“The dog was strong enough to be dragging three officers into the road. It’s so, so sad.”
Floral tributes to the child and family have already been left at the home in Welfare Road, Doncaster.
“Absolutely devastating,” one said. “Two parents have just lost a child and three other children a brother in terrible circumstances. Sleep tight little man.”
According to the Daily Mirror, the mother had recently suffered another tragedy, when her partner and father of her three older children died about 18 months ago.
One neighbour told the paper: “"It is heart-breaking, it's just shocking. It's a tragedy upon a tragedy.
"Her previous partner was such a loving father and appeared to be great around the house, we would always see him hanging the washing out and doing his bit.
"They just looked like such a lovely family, they were always together and always happy."
Detectives investigating the case have asked for anyone with information to contact them by calling 101.