While raising her children, Anthea recalled she had been in and out of domestic violence refuges. She had couch surfed at the homes of friends and relatives. She had slept in her car.

After moving from the Gold Coast to Brisbane, Anthea and her children were homeless again when she sought help from the Brisbane Homeless Service Centre in South Brisbane.

"They were really cool," she said as part of a Micah Project – a community organisation devoted to promoting social inclusion and justice.

The family had a place to call home. There was furniture, school uniforms, counselling, ongoing support.

She had a message for other woman in violent situations.

"Don't think you're the only one,"  she said in the Micah article. "There are plenty of other women going through it, too."

And she posted affirmations on social media about surviving domestic violence and her love for her children.

"Children shouldn't have to sacrifice so that you can have the life you want. You make sacrifices so your children can have the life that they deserve" – her final post days before her death.

As her daughters aged 11 and 12 slept nearby, 34-year-old Anthea was discovered unconscious in the lounge room of her rental property in Norman Park in Brisbane's inner east on Tuesday.

"Horrendous. It's their mother, absolutely horrendous," Detective Inspector Rob Kemp said. The woman's three-year-old son and eldest daughter, aged 15, do not live at the house.

Detectives are now searching for 38-year-old Gold Coast resident Jacob Michael Smith, eager to speak to him about the mother-of-four's suspicious death.

Mr Smith, who has been described by police as a friend of the slain woman, is known to frequent Brisbane, particularly the Wynnum area.

"He is a person of interest in this matter. He was there last evening from what witnesses have told us, so we're calling on him to come forward," Inspector Kemp said.

"He could've been there around 2am.

"All I can say is he's known to the person. He's been there before."

Mr Smith was seen leaving the woman's house between 3.30am and 4am, but police have not yet confirmed whether he left the property on foot or drove away in a car.

"He was there last evening, for how long we don't know, but we certainly would like to speak to him," Inspector Kemp said.

Police warned the public not to approach Mr Smith, but noted they were yet not sure of his involvement in the case.

"If this person is involved in it we are mindful that he could be a danger to [the] public. We just don't know what his involvement is until he comes forward," Inspector Kemp said.

Fairfax Media has not disclosed information about Mr Smith's background for legal reasons.

He is described as 180cm tall, of average build, and with dark brown hair.

Detectives spent the day doorknocking neighbours in a bid to locate Mr Smith.

Investigators also intend to interview the woman's daughters and speak with the woman's former partners.

Inspector Kemp said police were treating the death as suspicious.

"Our forensic police are still examining the scene...there's no extreme violence evident," he said.

He said none of the residents heard a disturbance and police did not believe a weapon had been used.

An autopsy on the mother-of-four will be conducted on Wednesday to determine the cause of death.

Police established a crime scene on Tuesday, as forensic officers dressed in blue suits examined the house.

The Milsom Street home sits opposite a sporting field and within walking distance of the Norman Park train station, about five kilometres from the CBD.

Neighbours were reluctant to speak to media on Tuesday morning, but nearby resident Linda Bright said she was "shocked" to hear of the woman's death.

Ms Bright said she walked past the home most days on her way to the local shops.

"It's normally a pretty quiet house...You never really see much movement or never really see people coming in or out," she said.

"We sometimes wonder if anybody ever lives there."

Anyone with information is urged to contact Crime Stoppers on 1800 333 000.

Kristian Silva, Danielle Cronin, and Marissa Calligeros