The Mackay parents of a "gravely unwell" toddler, who died after they allegedly failed to get her medical treatment, believed she may have been teething at the time, a court has heard.

Details about the days leading up to the death of Diana Hanbury were revealed during a bail application for her father Adam Hanbury in Brisbane on Tuesday.

His two-year-old daughter was not breathing when she was taken to hospital in December 2022.

Despite resuscitation attempts, she was unable to be revived.

The 37-year-old and his wife Jessica Hanbury, 38, were charged with her murder more than a year later under a recently expanded definition of the offence.

They were also charged with failing to register her birth.

The Supreme Court heard the crown will allege "they each failed to obtain medical treatment for their daughter when she was gravely unwell and in this way showed reckless indifference to her life".

Before she died, the court heard it was alleged Diana had been sick for about five days, and during this period her parents thought she was teething or suffering a "reasonably common" illness, which others in her household had recently recovered from.

The court heard her parents had allegedly made "some efforts" to address her symptoms, including administering pain relief medication, but on the day she died her condition had "deteriorated significantly".

Mr Hanbury's lawyer Ruth O'Gorman told the court Mr Hanbury was at work when his daughter was taken to hospital by his wife.

"With the case against Mr Hanbury, he is in a better position … in the sense that he did not have Diana in his care in the critical hours prior to Diana's death," she said.

Ms O'Gorman told the court a report from a practitioner also puts the case against him in doubt, because prosecutors would have to prove he would have known his inaction would "probably cause her death".

"Not only is the crown case in respect to murder not strong, but it's also not strong in respect to the … alternative of manslaughter," she said.

His application for bail was unopposed by prosecutors, but the court heard "the expert evidence will be important" during committal proceedings.

Mr Hanbury was given conditional release to live in South Australia with his family.

He must report to police there three days a week and can have no contact with witnesses or his wife, who is also on bail in Mackay.