Moving into residences
University residences and colleges usually provide you with some basic furniture - a bed, desk, set of shelves etc. Check with your residence to see what they do and do not provide.
Given the small size of most dorm rooms, you'll only want to take the essentials - a computer, books, stereo, clothes and a few sentimental items to remind you of home.
Hopefully, your parents will hold on to the rest of your stuff, but if not, how about putting it in storage?
Moving into a share house
A share house allows you to live cheaply but has a lot more space than a dorm room. You'll usually need to provide all your own furniture, so in most cases, you can just shift everything from your room at your parents' place to your new house.
Ask your housemates what shared items (TV, microwave, washing machine, couch, etc.) they already have, and which ones you can provide. You'll probably want to save your money for rent and/or beers, so a budget removalist is a good choice when moving into a group house.
Moving into your own place
If you're lucky enough to have your own apartment while you study interstate, you'll need to think about moving or purchasing several large appliances and pieces of furniture. A fridge, couch, bookshelves, TV and microwave are all necessities for a student's apartment.
Don't forget to organise the connection of your electricity, gas, water, phone and broadband a month or so in advance, to ensure you don't spend your first week of uni in the dark.
Compare quotes on interstate removalists to suit any budget.