I'm a Melbourne racer so welcome!
Don't even consider justrideit bikes if you want to race!
For well priced used track bikes (far better than new ones listed above) join up the following FB pages:
Australia wide = Bicycle Market
Victoria = Buy/sell road cycling Victoria
Australia wide = Track Cycling Marketplace and news
Plus check local gumtree ads.
What size bike are you riding (top tube length)? A number of Hillbricks and others around the price you are after listed recently on the fb pages which would be perfect for starting on. In regards to shipping, enough cheaper carriers like E-go.com.au, packandsend.com.au and grehound freight for interstate buys if nothing local.
Are you with a club yet? Worthwhile asking around there if you are, as many bikes get sold between members direct when riders outgrow their bikes.
If not a member yet, consider which club to join as some clubs have good junior track programs and have club bikes you can use for initial training sessions before you start racing. So don't let not having a bike at this time stop you from starting racing.
Feel free to ask questions about the local clubs and scene, as I race track year round as well as road, time trials plus CX...