The infant died on Tuesday afternoon almost a week after being taken to hospital with "significant internal injuries".
Uneeb Ullah, 28, was charged with domestic violence murder against a child overnight after being arrested in Ipswich, southwest of Brisbane.
He was not required to appear when his matter was mentioned in Brisbane Magistrates Court on Wednesday.
His case might return to court later in the day if new charges were laid, Magistrate Nicholas Brown said.
A police investigation was launched after the baby was taken to Ipswich Hospital on October 1.
The child had suffered "significant internal injuries", police said.
The toddler was later transferred to a Brisbane hospital where he succumbed to his injuries on Tuesday afternoon.
Detectives from the Ipswich Child Protection Investigation Unit, assisted by the child trauma unit, arrested Ullah that night, police said.
Investigations continue.
When Ullah's case came before the court on Wednesday, police prosecutor Ben Messina asked it be stood down until later in the day.
"I received a phone call this morning ... that potentially more material would be provided and asked if this matter be stood down to the end of the list," Sergeant Messina said of the "relatively vague request".
The magistrate agreed to re-mention the case if other charges were laid.
Kirstyn Nicholson, a Legal Aid solicitor representing Ullah, did not apply for bail and sought an adjournment.
Ullah was remanded in custody until the matter returns to court on October 26.
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