The father of a nine-month-old baby found dead on a Gold Coast beach, following what police say may have been a "sacrifice", has been extradited to New South Wales.

Key points: Police are awaiting the results of an autopsy being conducted in Brisbane

Police are awaiting the results of an autopsy being conducted in Brisbane A four-year-old boy has been taken into care

A four-year-old boy has been taken into care A 48-year-old man will appear in Tweed Heads court on Thursday

The baby's body is believed to have drifted in the water for two days after she was allegedly thrown into a harbour at Tweed Heads by her father, the ABC understands.

Investigations commenced after her body washed up at Surfers Paradise beach where she was found after midnight on Monday.

Her 48-year-old father, who cannot be named for legal reasons, was extradited to Tweed Heads Police station on Wednesday night after he appeared in a Gold Coast court.

He pleaded guilty to an unrelated public nuisance offence and the court was told he had a history of street offences and mental health issues, including schizophrenia.

He is yet to be charged over the baby's death.

Detectives are investigating whether the father, who is homeless, allegedly "sacrificed" the child, whose pram was found on the water's edge near Jack Evans Boat Harbour.

The parents of the child were known to police, and were found in Broadbeach on Monday along with a four-year-old boy who has been taken into care.

Detective Chief Inspector Brendan Cullen said divers were searching the Tweed River and Jack Evans Boat Harbour.

"The full circumstances of how that child got in the water is unknown. We're hoping divers may assist us, we're hoping members of the public might assist us, we're hoping CCTV might assist us. These are the things that will piece together what's happened here," he said.

"An autopsy was held in Brisbane yesterday (Tuesday) — the results of that autopsy have not been completed as yet and we are awaiting those from pathology.

"That's extremely important information and that will assist our investigation."

The 23-year-old mother of the baby has been released from custody and is being assessed by mental health authorities.

Flowers, toys and balloons were left at a memorial at Surfers Paradise where a nine-month-old girl was found dead. ( ABC News: Jennifer Huxley )

'Extremely complex investigation'

The family of four was tracked on CCTV travelling from the Gold Coast to Jack Evans Boat Harbour on Saturday and Queensland police then captured images of the three of them catching a bus at Coolangatta, sources said.

Police sources in Queensland alleged the mother admitted to knowing about the planned "sacrifice" but only the father would be accused of throwing her into the water.

Detective Chief Inspector Cullen said New South Wales Police had been working closely with Queensland police.

"Those investigations have led police to a very strong geographical nexus with New South Wales, and in particular Tweed Heads and we believe at this stage the nine-month-old child passed away in Tweed Heads," he said.

"The circumstances, the time and the place of where that actually happened is still under investigation.

"This is an extremely complex investigation as it crosses jurisdictional boundaries, time zones and has made what is a very tragic investigation even more complex."

Willem Ungermann saw the mother changing the nine-month-old in the last week. ( ABC News )

Tweed Heads resident Willem Ungermann said the baby's parents regularly frequented the park near the Jack Evans Boat Harbour.

He said he had seen the mother changing the nine-month-old in the last week.

"They seemed like normal people. We said 'hello' and stuff like that," he said.

"They looked totally fine."

Mr Ungermann said the couple lived in a van, and said there had been a spike in homelessness in the area.

"It's got very, very bad over the last two years."

Kirsty Davis said she knew the couple for a short time and she had held the baby on Saturday.

"On the Saturday the mother and father passed it into my arms … I held her for a while, comforted her," Ms Davis said.

She said she was now "traumatised and devastated" knowing the baby was dead.

ABC/AAP