Two children who were taken to hospital after their father allegedly doused them in petrol and set their sister alight in the Perth suburb of Doubleview have been discharged from hospital.

A seven-year-old girl was burned when her younger sister was allegedly lit on fire by 43-year-old Edward John Herbert at a house in the early hours of Saturday morning.

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It is alleged Herbert poured petrol on the three-year-old girl while she was lying in her cot in the middle of the night.

An off-duty police officer who lives opposite the house rushed to the scene and found the younger girl alight.

She remains in a critical but stable condition in Princess Margaret Hospital (PMH) with burns to her face and upper body.

The seven-year-old girl was discharged from PMH on Sunday.

The third child, a six-year-old boy, was not burnt and has also been discharged from hospital.

Police had earlier said he was being cared for by family.

Herbert made a brief appearance in Perth Magistrates Court on Saturday in connection with the incident.

He did not plead to five charges, including one count of aggravated grievous bodily harm and two counts of attempted grievous bodily harm.

Herbert is also alleged to have been armed with a knife during the incident.

He was shirtless, incoherent and humming to himself during his court appearance, and was held up by two officers and unable to respond to the charges due to his mental state.

– ABC