The man, from Kaiapoi, 15km north of Christchurch, was on medication at the time of the murder, and an outpatient at Christchurch's Hillmorton Hospital.
He pleaded guilty last month after being found fit to plead by a psychiatrist and was due to be sentenced at the High Court in Christchurch on Thursday.
But today in a surprise hearing before Justice John Fogarty, Thursday's sentencing was cast into doubt.
The man's lawyer Tony Greig asked for a psychiatrist's report under section 104 of the Criminal Procedures (Mentally Impaired Persons) Act to be considered before his client can be sentenced.
He said his client suffers from a "significant depressive illness" which needs to be taken into account when sentence is imposed.
But the victim's family have made plans to be at court on Thursday.
A number of them plan to read out victim impact statements and see justice being served. One family member is travelling from Australia.
Justice Fogarty proposed sentence to go ahead as planned, and to impose the mandatory life imprisonment, but to then adjourn to a later date to allow for the report to be completed before deciding the man's minimum period of non-parole.
The judge asked for the new psychiatric report to consider not the offence or its gravity, but to provide an "appreciation of his state of mental health" at the time of the murder.
The report should include notes on why he was still on medication, why he was at outpatient at Hillmorton when the murder occurred, and any other clinical observations which would assist the court in judging "to what extent his history of depression and associated episodes" should be taken into account in assessing a period of imprisonment.
Crown prosecutor Anselm Williams said he would like the police to speak with family members to see if they are happy with that, before making submissions.
If they wanted to wait for the psychiatric report, sentencing could be put off to a later date.
It was up to the family to decide, Justice Fogarty said.
The Crown has until noon tomorrow to speak to family members and come back to the court with a decision.
Final suppression orders would be made after Judge Fogarty considered new legislation.
But he said he was "currently favouring the view" that the man's name would not be suppressed, but the victim and girl's would be.
Mr Greig said his client, who wanted sentencing to go ahead as soon as possible, wanted name suppression, not for him, but for the victim and little girl.
