Moving to Australia from NZ

I am planning on moving to QLD from NZ with my children. I am a single parent who works full time.

What are my childrens rights for schooling and University (they are all nz born). Here in NZ, australian children have the same rights to free education etc or would they be considered international fee paying students?

I will be selling up here with the intent to purchase a property in australia. What are the rulings on that, being a NZ i know I can live and work fine, do I need to be there for so long before purchasing a house, and if I was needing to take out a mortgage (once a job was sorted) what are mortgage requirements. If I choose to rent, what information (other than rent and bond) would I require as I dont have rental references to provide.

I have already opened a bank account and will start depositing money in it to show a savings history, we are coming over at the end of this month where I will verify it and to have a look around as to what part of queensland we would like to settle down in etc ( or narrow it down :) )

For those with families that have moved over, what do you recommend, shipping your own furniture or just selling everything up and starting from scratch. ie is there quite reasonable second hand furniture stores around to get the basics until I am settled with job etc.

My ex husband is on the birth cert of only one of my children (though dna etc on the others - he was lovely lol), anyway he is currently serving a long prison sentence for horrific child abuse, I have full and permanent custody and protection orders, custody order states he is not allowed access or contact with the children. I am wanting to move to australia before he qualifies for parole for my childrens safety (he believes he must get payback for them testifying against him). Will I be able just to move over, even if he went back to court he would still not be allowed to see or speak to them. Its not a case of him losing contact or access with the children, he has had none for 6 years in fact my 7yr old has no knowledge of him. Only 2 of our 4 children will be under the age of 16 at the time we move.