It's alleged the woman took her two sons to the river about 5.30pm on Thursday.
Shortly after police received information the five-year-old boy was missing in the Murray River.
"The dog is four years old and it's never attacked one person, has grown up with kids, and it's always been around kinds playing", she said.
Marine Rescue NSW search the Murray River in Moama this morning.
She faced an extradition order by video-link in a Bendigo court on Friday afternoon, when it was agreed she would be sent to Deniliquin to face a charge of attempted murder of her older son.
The 27-year-old woman didn't appear before Deniliquin local court as expected on Saturday morning after requesting to stay in the custody cells.
The mother appeared before the court earlier on Saturday where she was formally refused bail, according to NewsCorp.
The Deniliquin woman, aged in her 20s, was extradited from Victoria to New South Wales on Friday night and charged with the attempted murder of one of her sons.
"We anticipate there will another charge", the police prosecutor told the court.
That nine-year-old boy is now far away from the river, in a hospital bed in the Royal Children's Hospital in Melbourne in a serious but stable condition.
As she was allegedly attempting to drown her sons, a pit bull dog belonging to a nearby resident was somehow alerted to the commotion and became involved.
At 10pm Thursday, as the search continued, a 27-year-old female relative of the children handed herself in to police at Echuca.
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That same night, a nine-year-old boy, his older brother, was being rushed from the scene to hospital with serious dog-bite injuries.
Dale Brooks, representing the children's grandmother, said the boys' mother had been living in a caravan on the back of the grandparents' property in Deniliquin since she was released from jail in February. He was last seen floating face-down in the river.
"What's really, really troubling about it was neither the police nor the Department of Corrective Services or Family and Community Services actually considered the risk to these little fellers", Mr Brooks said.
Detective Sergeant Swinton of New South Wales police said the suspect admitted trying to kill both her boys and allegedly told of having to "drown her babies" to witnesses.
UPDATE 10.15am: The woman remains under Victoria Police guard at Echuca Hospital this morning.
As he ran up the bank, he was "savagely mauled" by a dog, who then attacked the mother as she turned her focus to her youngest son. "We want answers", said the woman's aunt, who can't be named for legal reasons.
Despite the grandmother taking out an apprehended violence order against the woman previous year, authorities still expected them to live together.
"She is confused and upset", he told reporters.
The daughter then "snatched" the children in the grandmother's vehicle.
"I think they (the agencies) have some culpability in this case".
Deniliquin Superintendent Paul Condon said the tragedy will be felt around the country. She was released and then went to the police station for questioning.
The incident happened at Moama, near the Murray River.