Blake Matthew Seers, 38, allegedly killed his fiancée Kate Paterson and the couple's 11-month-old daughter April at their home in Logan on Thursday.
The tragedy was discovered after Seers was struck by a car not far from the grisly crime scene, 30km south of Brisbane.
Police were trying to contact his next of kin when officers discovered the bodies of his fiancée and baby girl in the family's home.
Both died from critical injuries from an edged weapon, police said at the time.
Witnesses raised the alarm after seeing a man covered in blood running along a footpath before he was hit by a black utility about 300m from the family home.
A trail of blood was marked along the footpath, leading from the house in the hours after the killings.
Seers remains in hospital and did not appear as two charges of murder were mentioned in Brisbane Magistrates Court before being remanded to the Beenleigh court on March 25.
Defence lawyer Nicholas Andrews said Seers had been diagnosed with schizoaffective disorder and would need medical support in custody.
The disorder is a chronic mental health condition combining schizophrenia symptoms, including hallucinations and delusions, with episodes of depression and mania, according to Queensland Health.
Outside the court, Mr Andrews said it was a sensitive matter.
"Our thoughts are with those families and people affected by this tragedy," he said.
"But at times like this, I just need to remind myself that there is a job to do.
"There are mental considerations here and we will be ensuring that those are raised through the appropriate legal channels."
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