I just checked the ICAA website and there is a tertiary qualification i.e. degree route too. Came as a surprise to me.
I echo the others in terms of having ACCA or CIMA though to help your employment prospects down the line.
I know what AAT is but doubt many Australians would however or they would probably treat it like a Cert IV which is a bit like HND level if those still exist in the UK.
CIMA has an advantage over ACCA in that you can obtain CPA through mutual recognition, or at least you used to. Not sure if they extended the period that they were granting it for as it is a while since I did this.
CIMA is also "easier" than ACCA having seen what my OH had to do compared to my syllabus. That was a good few years ago though so may have changed.
Good luck with whatever you decide to do.