Are family support payments available for new arrivals that haven't yet found work, coming from New Zealand? Also are rents competitive in Adelaide? Will we find a rental relatively easily and cheaply? Thank you.
There are some family assistance payments available that you can apply for here: http://www.familyassist.gov.au/payments/family-assistance-payments/
The best place to get an idea of rental prices in Adelaide and how many properties are on the market is on RealEstate.com.au. Rental prices there are generally cheaper than other major Australian cities, I'm not sure how competitive it is though!
Just a tip, it will be easier to get a property if you can both show you are working.