One of the best places to go paragliding isn't in Melbourne itself; Active Flight is around a three and a half hours drive from Melbourne. You receive de-briefs from your pilot and this organisation provides a really adrenalin filled tandem paragliding experience. Expect to fly on the safest harnesses and receive expert guidance. Paragliding courses are also available in increasing your self confidence. Apart from the tandem paraglide; there are other flight options available, and the basic flight is the most recommended paraglide initially as you are done within 10 minutes, and the fear factor begins to diminish with more practise.
Otherwise if you want to try paragliding closer to home, then Adventures Today is a great source of information to take your research further which includes 1-hour paragliding courses and other tandem paragliding experiences.
Before diving into the deep end, you can also learn Paragliding for for a 2 day free trial at High Adventure paragliding school based closer to Sydney. There are Victorians who have travelled in order to experience this. For cheap paragliding experiences, Groupon is another great source.
Other great Paragliding sources, especially if you want to take things further and become a Paragliding pilot would be at the Paragliding Headquarters. Ensure you are healthy and well prepared. Otherwise happy Paragliding.