Mrs Burke asks why families with young children should have to suffer in damp, cold homes because they cannot afford to spend $400 on rent.
The family moved to the area about a year ago from Invercargill, where they owned a house, because there were better work opportunities for Mr Burke, who is doing a panelbeater's apprenticeship, and to offer their children better opportunities.
With Mr Burke, 28, on an apprentice wage, Mrs Burke, 25, works part-time and their income goes towards supporting the children and paying bills.
"I've never set foot in a club in Queenstown ... we're just focused on our family and getting somewhere.
"I know people don't want Arrowtown to change, but it's 2013, places do change, they do go forward and I think this is a step in the right direction."
Tenants would live in the reduced-rent homes for up to five years, with the intention of saving money towards buying a home in the district with help from the housing trust.
Mrs Burke said the scheme would provide homes for people already in the area rather than bring an influx of people into Arrowtown, which is a concern from those in opposition.
"If we could get one of those homes we would be in there in a heartbeat, but we have seen how long the list is."
She said they had known the cost of living in the Queenstown area but considered it "short-term pain for long-term gain".
During question time in Parliament on Wednesday, Housing Minister Dr Nick Smith said he was "appalled to read that some residents were using council processes to oppose this housing, saying they did not want low-income people living in that town".
"We need to stare down this sort of nimbyism," he said.
With the cabins scheduled for removal, Mrs Burke is relieved the family has found another Arrowtown house, within their price range but also two bedrooms, which they hope will be warmer.
"If it was just Matt and myself we wouldn't worry about it, but we've got little people too."