But they say increasing rental prices mean that will not be happening any time soon.
Dunedin had the biggest increase in median rental prices last year — up 12.9% according to the New Zealand Property Investors Federation (NZPIF).
The pair had to leave their Forbury flat in February and are now boarding at some friends’ house in North East Valley.
"I’ve spent the past few years boarding with friends and my sisters ... it’s more something you do when you’re younger.
"But once you get older, you kind of need to have your own privacy."
Ms Dunlop said the price they could realistically afford was $250 a week and at a push they would pay $400.
"For the last couple of years me and my partner have been struggling to find a place in Dunedin that’s a one-bedroom, two-bedroom, that’s cheap enough for us to afford. It’s quite hard."
They live off of one income from Mr Wi Parata’s job as a security guard.
As of yesterday there were 101 Dunedin listings for two and three-bedroom houses for rent online and of those just 23 were below $400 per week.
"We are thinking of putting it off for a couple of years because of how expensive it is," Ms Dunlop said.
Even when there are places that are within their price range, Ms Dunlop said there were often other obstacles in their way.
"When there are cheap places ... they may be cheap but then they’ve got all these ‘no pets, no this, no that, no couples’ ... in Dunedin especially a lot of places won’t take couples.
"It’s quite intense."
The NZPIF has blamed the rental increases on new tenancy regulations such as compulsory insulation and smoke alarms.
"We were accused of scaremongering when pointing this out a few months ago, but the facts show that we were right," NZPIF executive officer Sharon Cullwick said.
But Ms Dunlop said she was not seeing enough improvement in rentals to justify the increase.
"There’s still a lot of private landlords who don’t even follow those [regulations] to this day.
"There’s been a few properties that I’ve lived in in the past that should have been condemned. Mould, damage to the kitchen, broken appliances supplied by the landlord."
Otago Property Investors Association president Kathryn Seque said the recent rise in rental prices in Dunedin was down to the city catching up with other main centres where rents had been a lot higher.
