yes plenty of people do this route, and there will also be plenty travelling alone so you will be fine.
3 weeks is ample time. I would spend 2-3 days doing the Great Ocean Road, then spend some time in Melbourne and visit some other places in Victoria such as Wilson's Promontory National Park (stunning) and Phillip Island to see the penguins. if you like walking you could even go to the Grampians for a few days. from Melbourne you could either hook up with other travellers as heymonkee suggested, which you should be able to do through looking at hostel notice boards where people tend to advertise for other travellers to share gas with, or get the bus. I got the bus from Melbourne to Sydney with a stop in Canberra overnight to break up the journey, but if I had been able to do it by car it would have been better as there are more interesting places to stop than Canberra.