The 70-year-old former Newtown Jets rugby league player appeared in the Southport Magistrates Court on Queensland's Gold Coast, following his arrest, and applied to be bailed to live with his brother in NSW.
A podcast, The Teacher's Pet, brought global attention to the case this year.
The husband of Sydney mother Lynette Dawson, who disappeared nearly 40 years ago, has been charged with her murder.
In 2015, NSW homicide detectives established Strike Force Scriven to re-investigate the circumstances surrounding Lynette Dawson's disappearance and suspected murder.
He has said that she abandoned the family for a religious group, the BBC reported.
Mr Fuller said detectives received additional evidence since asking the Office of the Director of Public Prosecutions (DPP) to review their brief of evidence in April.
Police will use previous interviews they had conducted with Mr Dawson since his wife's disappearance as evidence in the case.
He said media reports had contributed to officers gaining additional statements relating to the disappearance.
Detectives allege Mrs Dawson was having financial trouble when she disappeared and will argue that, because she had organised a family portrait and her children were due to return to school, she did not plan to disappear suddenly of her own accord.
Police press conference regarding the arrest of Chris Dawson
Speaking on Studio 10 on Wednesday, Lyn's brother Greg Simms - the first of her family to be contacted by police today- said the family were "over the moon" about the arrest.
He also described the police case as "circumstantial", as no body had been found.
Queensland Police said Mr Dawson's extradition to NSW was unlikely to take place on Wednesday because of continuing negotiations with the commercial airlines over security arrangements.
"I wouldn't have written to the DPP otherwise", he said.
"There are other examples in policing history, and history of the courts, where people have been convicted of murder without a body", NSW Detective Superintendent Scott Cook told reporters on Wednesday.
Chris and Lynette Dawson on their wedding day.
"We have no doubt whatsoever that Chris will be found not guilty as he is innocent".
Fuller said authorities have not located Dawson's body, and that finding her remains is "not crucial to finalising the matter", but maintained "we certainly won't give up on that search".
"Its taken a long haul but its going to be a very good Christmas for our side of the family knowing that we've finally got somewhere and we're going to find out what actually happened through the court system", he told the program.
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