Note: I am in the UK. I don't know specifically about australia but I expect the general principles will be much the same everywhere.
What banks want is to be reasonablly confident that you have a steady income stream that will continue to pay the mortgate until it completes.
In general employed are fairly easy to assess. Most employed people will have a steady basic pay that increases through their career. Payslips will usually seperate-out basic pay, overtime and bonuses. There is little opertunity to cook the books.
The self-employed are harder to assess. Income can be bursty and there are far more opertunities for cooking the books to make it look like you are earning more than you really are.
So banks are likely to be far more careful about lending to the self-employed, they will likely want to see multiple years of buisness records so that any bursts, whether natural due to the ebbs and flows of buisness or deliberatly created to cook the books average out and they can see the overall pattern.
A large deposit will help because it reduces the risk to the bank in the event of a default. Similarly not being anywhere near your limit of affordability will help.