Gregory Keith Davies, 74, was attacked at Port Philip Prison in Australia in July and is now in “extreme discomfort” after his skin was burned.
He was due to be in court later this month for a plea hearing and to be sentenced for the sick murder.
However, his defence lawyers have argued for an extension because of the scale of his injuries.
In May, Davies admitted to assaulting and killing Kylie in a suburb, north of Melbourne in Australia 33 years ago.
The young girl had been sent by her mum Julie to get sugar but she never returned.
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After she was abducted, raped and murdered, her body was dumped in a gutter more than a mile from the corner shop.
The murder remained a mystery for more than 30 years until new DNA evidence found from semen in the victim’s underwear led police to Davies last year.
The defence lawyer for Davies, David Gibson, said: “He is in extreme discomfort, he’s had skin grafts to 15 per cent of his body.
“Those grafts are now tightening up and causing him considerable pain.”
When Davies was arrested at his retirement home, her mother Julie Maybury said: “Nothing will bring Kylie back, but having somebody charged is a great result.
“There has never been a day since 1984 that I haven’t thought about Kylie and looked for ways to get justice for what happened to her.”
Justice Lex Lasry said he couldn’t refuse an adjournment, and Davies will now appear on November 27.
According to the Australian Associated Press agency, no charges will be brought against the prison attacker.