I believe there are some traineeships available in the market.
I suggests you to alter your search, not just looking for permanent full time job, also make yourself avaliable for contracts / temp job.
My very first job after uni was on 6 weeks temp basis cover wedding leave, but extended immediately after entering the company for a 6 months contract. and I left that company when the contract ends to get another better permanent job.
There are way a lot of more opportunities once you get into the company. ( my current employer offerred permanent jobs to the temps after they shown the managers right working attitudes etc. )
You have advantages over to people who migrated here with overseas degree, as you graduated here with good English and knowlege of local tax laws and accounting standard etc.
Be patient but be preapred as well!!
Also, go to get someone professional to edit your C.V before you sending it to any employer / agent. it will help you a lot!