Mr Baxter's wife Hannah and their three children were killed by the blaze on Wednesday. He also died at the scene.
Some Australian media say he doused the white SUV in petrol and set it alight before stabbing himself.
But police say it is too early to be sure how the fire started.
"How the fire actually occurred has not been ascertained at the moment so for us to call it a murder-suicide or a tragic accident, it's inappropriate at this stage," Detective Inspector Mark Thompson said.
He went on to say that while he had seen "some horrific scenes" in his job, this was one of the worst.
Police were first called to the scene in the Camp Hill area in the east of Brisbane at 08:30 local time on Wednesday (21:30 GMT on Tuesday).
They found the couple's three children Laianah, Aaliyah and Trey - aged between six and three - dead inside the car.
Emergency crews tried to revive Rowan Baxter, 42, but he was declared dead.
Australian media report that he was found close to the car with a self-inflicted stab wound.
His wife, Hannah Baxter, aged 31, died later in hospital from extensive burns. She had reportedly jumped from the car yelling: "He's poured petrol on me."
Rowan Baxter had been in the front passenger seat and his wife had been driving the car, police said.
The pair had reportedly separated late last year, and were trying to work out custody arrangements.
Paramedics said they had also treated a passerby, who had "tried his best to get to the car". He had suffered some "facial burning" and also been taken to hospital, a Queensland Ambulance spokesman said.
Rowan Baxter formerly played for the New Zealand Warriors rugby league team in Auckland and had also been running a gym called Integr8 with his wife in Capalaba to the east of Brisbane.
The gym's website describes her as "an enthusiastic, passionate mother of three" and a trampolining champion who represented Queensland for four consecutive years and also achieved international medals.