I would suggest talking to a charity, start with St Vincent de Paul) to see if there is any support available to you. If they cannot help, they might be able to point you in the right direction.
It seems odd that if it is a major operation there is no financial support available. Especially if you may be off work for an extended period. Do you have people, possibly family, who will be looking in on you ?
If it is a major operation like a hystorectomy, recovery is not something to be taken lightly. If anything goes wrong you need access to assistance.

When you can get into centerlink make sure you look into applying for the energy rebate through your energy provider asap (as it takes awhile to come through). That'll help with the following energy bill.

Hystericoctomy sucks

Use "half price"app and buy groceries only at 50% off.
Use " petrol spy" app to find cheap petrol.

Don't forget that you have to eat well during your recovery, including protein, because the repair of your body (wounds etc) will take a lot out of you. Most people lose some weight as the body utilises its reserves to close wounds & rebuild flesh.
And your body will crave what it needs. So have some good quality meat in the freezer. Alternatively make up meat based casseroles, and put them in individual serve lots in the freezer, so its just heat and eat.
Potatoes, broccoli, and cauliflower and peas can be included in the casserole. So easy.
If you are having an abdominal operation you will not be able to lift more than a pound of butter for the first 6 weeks. Otherwise you risk tearing wounds, and believe me that hurts.
Find out from the surgeon what is required for recovery. Also what you can do in advance to speed healing. I was instructed to take Vitamin C for a fortnight before the operation.

How much did it cost you to stock up on pads and tampons? Consider switching to a menstrual cup - initial outlay is a bit, but long run you save so much money. Save what you can, now. Revisit your budget and cut non essentials. Organise payment plans for things like gas, electricity, water and phones. $10 on each, or whatever, and you may be in credit on your account by the time it rolls round.
Meal prep and bulk out meats with beans and legumes. Shop specials. Use farmers markets.

Save as much of your current wage while you still have it. Eat more vegetarian meals. Look for free or cheap entertainment options especially those that may help secure another job.

Before your surgery consider any items you want to sell on gumtree or somewhere to put a little cash aside. Cook some cheap batch meals like bolognese sauce, soup or curry so you don’t have to cook when you are convalescing and stick them in the freezer. Careful with stuff like internet, phone and power use so you don’t get any big bills. Minimise your use of the car. Consider some short term small jobs to help in the interim like ironing or tutoring online English language students. Good luck with it all.

To save money on food, stock up on canned goods, tuna, baked beans, soups all help cut costs. It's daunting and it's scary but you will be amazed at how strong you are getting through it all. Good luck xxx