Blood tested for what? If you donate blood they do some basic testing for you. Otherwise I think you need a referral do you have Medicare? You can get a referral from a doctor pretty easy and sometimes you can get the blood tests on Medicare too.
As far as I know, you need a referral from a doctor. That was my case in Canberra. The referral costs you a doctor's visit, 85 AUD here, of which the insurance refunds some, depending on your coverage. At my cheap cover, I got less than half back from the insurance.
The blood test itself also costs money, which the insurance partly covers.