I am an NZer and was entitled to FTB when I was in Australia when my DS was born. Australia and NZ have a reciprocal arrangement for health and welfare. There is a 6 month (I think) stand down before you can get the dole and other benefits, but after that time you are eligible for all benefits. A NZer automatically has Permanent Residence, it does not need to be applied for. It is also only a few hundred to become a citizen, not the thousands for other nationalities.

Australia and NZ do not make you renounce your original citizenship to become a citizen.
we had cenetrlink ring up on our behalf and find out costs of cit and there were several payments to become one in total it was over 2000. Every time i go to centerlink i ask can dh claim any beinifts to be told NO. i wish he could at times.