Jodie Tarnawskyj, 35, was charged over the death of her baby, Oliver Izac Tarnawskyj, at her home in Paradise Point on June 8 this year.

Her arrest came at the conclusion of a long and intensive investigation by Gold Coast police, who executed a crime-scene warrant at her home on Friday.

As she is facing a murder charge, Ms Tarnawskyj was unable to apply for bail at the Southport Magistrates Court on Saturday morning.

No details about Oliver's death, or the police investigation, were outlined during Ms Tarnawskyj's brief court appearance.

Ms Tarnawskyj appeared distressed as she appeared in the Southport dock, silently communicating with a supporter in the gallery.

The man left the court without speaking, following Ms Tarnawskyj's appearance.

Barrister Charles Bagley, for Ms Tarnawskyj, requested the matter be adjourned until early next month for mention, but magistrate Jacqui Payne said she preferred to proceed straight to a committal mention "to get the ball rolling".

The court was told police were waiting for more forensic results, which could take up to three months to come back.

Ms Payne set the committal mention date for February 2 at the Southport Magistrates Court.

Ms Tarnawskyj is expected to apply for bail in the Supreme Court.