In the US context there's a straightforward way to reduce education expensives for doctors. Make medical school not require a bachlor degree but allow students straight out of high school to go to medical school like it's possible in Europe. I don't know how the situation in Australia looks like.

Professional bodies often prevent nurses from doing many tasks for which they are qualified. Allowing cheaper nurses to do more tasks would reduce costs. Professional bodies also limit the amount of new doctors. As a health care priority we likely want to train more doctors than we currently do. You can't simply hire more doctors when you free up money by paying doctors less. There a limited amount of doctors trained and when you have lower pay as a doctor it will be more attractive for them to switch careers.

When it comes to waiting times it's also worth remembering that they aren't always bad. The reduce incentives for overtreating patients. A while ago a doctor told me about health care economics: "Every hospital bed finds it's patient." Doctors have a lot of power to advice patients to engage in medical interventions and when a doctor has a lot of free slots he is likely to talk patients into treatments that aren't good. When the doctor has a waiting list he thinks a lot more about whether the intervention is actually good for the patient. He then acts more as a good advisor then as a surgery salesman.

How can hospital emergency department and surgery waiting times be cut?

At this point, there hasn't been a lot of analysis about why waiting times are as long as they are, so start by taking a detailed look at the procedures.

Cut doctors pay and hire more?

The supply curve typically slopes the other way.