NZ Family Trust Advantages and Disadvantages in Australia

Hi, I am currently living and working in NZ and plan to move to Australia in the future. My wife and I own a family home together in NZ and don't currently have any family trust. We also have an seven-year-old daughter. I have a couple of questions below:

• should we create a family trust in NZ, sell our family home and put and gift all the proceeds into this new family trust before we move to Australia?

• is there any disadvantage/advantage for a NZ family trust used for owning a family home in Australia? I understand (I could be wrong) family trust is a familiar concept in NZ but not in Australia. There is no capital gain tax for a family/residential home in Australia but not sure if it is owned through a family trust. I assume stamp duty is the same for all ownership structure used for owning family home. Also, currently NZ superannuation are not income and assets tested but Australia superannuation are income and assets tested. I read somewhere that a trust (family trust?) will be taxed higher in Australia (I can't remember anymore to what context is the tax higher(income/capital gain tax?))

Let me know if anyone has any experience with this or can refer me to the related article links. Thanks in advance.