Henry Shepherdson, 38, was seen by witnesses to jump from the Whispering Wall at Williamstown on Wednesday afternoon while holding nine-month-old Kobi in a child carrier.
They died at the scene.
Police released their names on Thursday and Kobi’s mother supplied photos of her daughter.
Assistant Commissioner Ian Parrott said there was some history of domestic violence in the family, but Mr Shepherdson had lawful access to his daughter.
In a statement, SA Police said early investigations had “shown a history of domestic violence between Henry Shepherdson and the mother of Kobi”, adding that “no one else is being sought over the deaths”.
“Obviously this is a highly distressing and emotional set of circumstances,” Mr Parrott said.
He said the mother was not present at the dam but had called the police emergency line within a short time of witnesses also calling triple zero.
“Clearly, they have had a child together, there was a relationship there but something has happened within that relationship,” he said.
“For reasons that I think all of us can’t fathom to understand, it’s resulted in this tragedy.”
Mr Parrott said police are investigating the circumstances of the deaths, and a report will be prepared for the coroner.