Possible with Youth Allowance + casual work here and there, difficult and probably impossible if you can't get youth allowance if you're doing something like Science.
With a low contact, low-ish workload degree like arts or many business sort of degrees you can work a fair bit but for Science/Engineering where you might have 20 contact hours then lots of additional study time and assignments on top, it'll wear you out very quickly.
People will come onto forums like this or onto reddit and tell you how they worked full time while studying a hard science or engineering and how it's totally easy do-able and everyone else is just lazy... those people are lying, or using some silly logic along the lines of "I worked 3 hours a day five days a week while living with my parents and five days a week = fulltime."
The most major problem isn't there not being enough hours in the week though, it's that you're 100% dependent on actually having work and in reality you might not be able to get it, or to get enough, or you might have a job that fits then have your hours cut a week before exams.
10 years ago you'd have been fine, you could work on the assumption that you could get a cafe/supermarket job or two and get as many hours as you needed, and if things went bad somewhere you could find another but it's not like that anymore. There are tons of unemployed people who are fully available and desperate for work competing with students for jobs, and foreign students, backpackers and other immigrants working for bellow minimum wage being paid under the table.
The industries that students traditionally worked in are completely stuffed now when it comes to pay/conditions and being able to reliably get work. You simply can't rely on being able to get a casual job you can fit in with uni within a couple of weeks anymore.
You really need the base income of youth allowance to make sure you can pay for rent+food, then work when you can, try to keep at least a couple of thousand in savings going into semester and draw down when needed.
Also the idea of having your own place is sadly fanciful, you'll be living in a sharehouse most likely. (if you're looking at ANU try and get into a college, it's really the only reason to go there)