You're Canadian so you're used to long lonely roads, but this can be a really looooong trip. Melbourne to Cairns is over 3000 kms (that's 1800 miles). Fortunately we have some of the greatest beaches in the world along the way, plus wine regions, major cities and quiet rural areas.
Consider hiring a campervan (mobile home) so you can stay at some of the more remote places... hotels and motels are not always the best option.
Melbourne has great shopping, fabulous restaurants and a great nightlife as well as art galleries. If you head north (in summer) consider driving the Alpine Way, it'll take you up to Mt Kosciusko (our highest point) which you can hike relatively easily. Sydney is our biggest city and sits on a beautiful harbour. Do the bridge climb. Go see a performance at the Opera House. Get someone to take you sailing on the harbour.
A couple of hours north is the Hunter Valley wine region.
Then there are brilliant beach towns all up the mid-north coast. See the big banana in Coffs Harbour. Byron Bay is a couple of hours north of Coffs. Or take the inland route and see some of our country towns, including the country music capital Tamworth.
Then into Brisbane, which has a vibrant food culture. An hour or two north of Brisbane is the Sunshine Coast.
You're now about half way to Cairns! With only 3 weeks I'd suggest returning the van in Brisbane and hopping onto a plane to Cairns where you can go and dive the Great Barrier Reef.
but that's just my suggestion.
Here're our travel safety tips for Australia.
Phil at the safety hub over 4 years ago
Three weeks will give you a taste of Australia, four might be better. You could drive from Melbourne to Sydney via the inland highway which will take about 9 hours. Two hours out of Melbourne are the fairy penguins down at Phillip Island. The Great Ocean Road is a beautiful drive, but two hours in the other direction. If you only hire one car, just think how you are going to fit 4 suitcases plus yourselves... Use google maps - "get directions" to map your way so that you can see how far you want to travel each day. If you go past Brisbane you might want to do a 4WD trip to Fraser Island. Noosa is a nice place to have a few days off. We do a lot of camping and our caravan parks are not like the US RV parks. They have a lot more room, possibly grass, large amenity blocks (not just two of everything!), they often have camp kitchens which is a good way to meet other travellers who will give you tips on where to go. Otherwise, Phil's ideas look good.
You haven't said what time of year you wish to come, covering that amount of coastline, the weather will vary quite a bit. over 4 years ago