Yazidi Iraqis Khalaf Smoki and Layla Mahmod have just purchased their own home in Wagga after significant personal sacrifice.

The couple fled persecution in Iraq by terror group Islamic State and moved to Wagga in 2017 with their young daughter Dima, now aged 5.

"Thank you so much to the Australian community for opening their country to us," Mr Smoki said.

"The Australian people are looking like my community. When you're talking to them, they smile with you, they're talking in a nice way to you."

They have been working tirelessly for the past two years to save enough money to buy their very own house and secure a better future for their family.

"We're very happy for the new house. But we have a very, very hard job ... We were working very hard, all the time saving, saving. And then we buy the house," Ms Mahmod said.

Mr Smoki works for Red Cross migrant support services full-time, as well as working a second job as an overnight cleaner.

Until six months ago the family only had one car, so Mr Smoki would walk 40 minutes every evening straight from one job to the next.

Ms Mahmod has also been working as a cleaner while caring for Dima, who will soon begin primary school.

As a religious minority, the family would not have been allowed to put their name to any legal documents in Iraq, even before the horrific genocide of Yazidis by the Islamic State began in 2014.

"This is a big day for the Smoki family, because this is the first time we have a house on our name," Mr Smoki said.

"Not my father and my grandfather, my whole family don't have a home in their name. They don't have a certificate [of homeownership] like ours."

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The Smoki-Mahmod family were forced to flee their home in Iraq for a refugee camp in Turkey, where they lived in a tent while Ms Mahmod was sick with an undiagnosed illness and Dima was a baby.

Three years ago they were accepted by the Australian government to resettle in Wagga as refugees and arrived without knowing any English and without any connections to the community.

"It was very hard. When we come here, we never speak English," Mr Mahmod said.

"Then I said to Layla, 'We should be working. Because we came to Australia and we need something for the future for the family."

A chance encounter at the GP's office in these early days saw the Smoki-Mahmod family form a close friendship with Wagga couple Bruce Leary and Helen O'Connell.

In the beginning they had to rely on Google Translate to communicate with one another, but Mr Leary and Mrs O'Connell are now like "a second mother and father" to the Yazidi family.

Mr Leary said he and his wife were extremely proud of the Smoki-Mahmod family for all they had accomplished.

"Helen has instilled in both these beautiful people a saying ... 'The harder you work, the luckier you get'," Mr Leary said.

"And that is exactly what they've done. They have worked extremely hard ... And what they are achieving is absolutely a credit to them from where they've come from to where they are now."

Little Dima said she loved Wagga and was looking forward to starting school in 2021.

"I like to be with my friends," she said.

Mr Mahmod considers himself fortunate to have had most of his relatives now join him in Wagga.

He said he was grateful to have had the opportunity to forge a new life in Australia.

"After we left the genocide [in Iraq], we had about five days sleeping in the street ... in Kurdistan cities," he said.

"Now it's a very big day for us - we have a house in Australia.

"Wagga is our dream."