$373 a week isn't enough to live on (Australia is not cheap). In addition to food, transport, utilities, rent, earning $373 means you are actually over the tax threshold so will be paying tax.
Even if you think your going to share a room with someone rather than having your own room, you will never be saving any money to pay for your next terms course fees, the expensive medical insurance that you will probably be required to get with your visa etc.
I think I was required to show evidence of 1 years fees - they did ask for some financial proof before granting my visa. It definitely wasn't 60k though.
PS Your 10k will also go a lot lot faster than you think. There were things I hadn't thought to budget for and others that just cost more than expected. Rent bond will eat a chunk. Its a struggle, and work is not as easy to find as you might think.