Lawyers for a former Adelaide woman who faces the death penalty in the US state of Arizona over her stepdaughter's death will meet with the consulate today to try and secure public funding for her defence.

Key points: Ex-Adelaide woman Lisa Cunningham's case has been adjourned until February

Ex-Adelaide woman Lisa Cunningham's case has been adjourned until February Ms Cunningham and her husband, Germayne Cunningham, have pleaded not guilty to 11 charges

Ms Cunningham and her husband, Germayne Cunningham, have pleaded not guilty to 11 charges Mr Cunningham's daughter Sanaa, 7, died in February 2017

Lisa Cunningham, 44, appeared in an Arizona court charged with the first degree murder of her seven-year-old stepdaughter Sanaa, who died in February 2017.

An autopsy found the cause of death to be sepsis related to a chest infection, an abscess in her right foot and multiple skin ulcers.

It was also noted the child had an unspecified schizophrenia spectrum disorder.

The Maricopa County Court was told the disclosure of key evidence was still ongoing between the prosecution and defence, but lawyers for Ms Cunningham wanted to hire their own expert to forensically examine her mobile phone.

Outside court, her lawyer Eric Kessler told media that his client, and her co-accused and husband, former police detective Germayne Cunningham, were "doing pretty well" and were settling into to jail while they awaited trial for 11 charges, including first degree murder and child abuse.

Sanaa Cunningham died in February, 2017, aged seven. ( Supplied )

"We were able today to successfully get an order from the court that would direct the medical examiner to give us certain slides from the autopsy, which would certainly help the defence pathologist help determine what the true cause of death was," he said.

"The cell phones allegedly contain damaging texts that are central to the Government's case, but when the Government initially hired an expert to extract that information from the cell phones, the report that was issued contained so many errors that it was deemed unreliable and worthless so the state had to re-test those phones and re-extract the information.

"Now the defence expert will have a crack at those same devices and will issue his report."

He said he was hopeful that information from the autopsy and phone would shed some light on the case.

"We're still trying to get clarification exactly what they did according to the Government that constitutes the child abuse that is at issue with respect to the homicide charge," Mr Kessler said.

"It's not clear what the cause of death is. We believe our pathologist will be able to shed more light on that.

"[Ms Cunningham is] doing quite well and she's participating in her defence. She's able to read reports. She communicates with us and from a health standpoint she's fine.

"I'll be meeting with a member of the consulate later today with respect to supplemental funding."

Trial expected to be heard in 2020

When asked if Ms Cunningham had already been provided with any public money to foot her legal bills, Mr Kessler said that would be discussed in meetings today.

Ms Cunningham will be back before the court in February while her trial is expected to be heard in July 2020.

Both accused have pleaded not guilty to all 11 counts.

Court documents allege the couple shut Sanaa in their backyard, laundry and garage, forced her to sleep outside, restrained her with cable ties and failed to seek medical care.

In August, the court ruled that both adults were eligible for the death penalty, remanding them in jail.