Yes, that's why the Australian health system is lucrative for doctors. Its a mixture of the Canadian and American health systems.
All medical procedures attract a medicare fee which is paid by the government. The doctor then decides whether or not they will accept this as the full payment for the consult/procedure (if the patient is in a public hospital, this is by default the full payment) however in a private consultation/hospital the doctor can decide to charge extra on top - and this can be payable by the patient (out of pocket) or by the patient's private insurance (if they have any).
The advantage of this to the doctor is they can keep charges in line with inflation, and see fewer patients for a given amount of income.
There are doctors who still operate purely bulk billing, but most operate on a combination of the above. For example they bulk bill pensioners and students, and have an extra charge for the rest of their patients.