We arrived in Brisbane in August. Got approved for mortgage in October based on a job offer letter. Conditional approval came about a week after I started work and before my partner had started (my job is permanent but hers is a contract role - they still took it into account) was subject to the bank seeing first payslips prior to settlement. Second tier lender, competitive but not market leading rate. Was pretty surprised by this but just different to the UK I guess where I doubt any lender would have touched us in a similar situation. Our situation sounds similar to yours - deposit 50% of the intended purchase price.
We used a mortgage broker - may have worked without one, dunno, but seems more common to use a broker here than in the UK.