Gold Coast to Melbourne in 2 weeks is very ambitious and I fear you would spend all your time driving. I have driven this several times...sometimes just to get to Melbourne and sometimes as a road trip. My preferred coastal drive is from Gold Coast to Sydney and then maybe consider flying from Sydney to Melbourne. It is a really pretty drive too but if I had to choose one coastline to see it would be NSW. I think you will have a much better time by covering less distance. Otherwise you will have lots of one night stays! Given the age of some of your group I think it would be worth reconsidering. Suggested stops between Gold Coast and Sydney are
Byron Bay, Coffs Harbour, South West Rocks, Port Macquarie, Forster, Port Stephens, Inland to Cessnock (Wine Region) Back to coast and on to Sydney. From Sydney maybe visit Blue Mountains. Spend some time in Sydney then fly to Melbourne. This Itinerary would have you driving 2-5 hours between towns. Hence why I would recommend cutting the distance down.
Hope this helps.