Skip Brisbane the weather here is not that bad. We get most rain in Spring and Autumn. The days are usually crisp and cold/cool depending on where you are from. Day time will be in the mid teens celsius and the rare night will dip below freezing mostly 5-6. It gets light at about 7.30 and dark at 5ish so there is plenty of daylight for you to be out and about.

So if you come from somehwere with real winters it will be mild. If you come from the tropics it will be freezing.

The great ocean road in winter is FANTASTIC!
ONE the Winter Antarctic storms send large waves pounding the coast but not the storms themselves. Great to see waves spraying over 30m cliffs.
TWO the crowds will be much less.
THREE there are plenty of wineries etc. to visit if the weather does turn agaisnt you. Likewise for Melbourne. There are plenty of quirky and interesting places to visit indoors.

Bring a scarf, a beanie, a coat and a sense of adventure and you will be fine.

Hi, I agree with peterSale. There is plenty to do in Melbourne and surrounds even in winter. Melbourne is often described as having four seasons in one day and in 2011 we even had hail on Christmas Day (usually 30+ degrees)!
I would suggest flying between Canberra and Melbourne (bus/coach) would be tedious. Avoid a Friday or Monday flight is you can, as it will be cheaper (a lot of people that work for the Aust Government in Canberra don't live there, so commute one end of the week). Try webjet.com.au
With regards to the Great Ocean Road, be aware, it's more than a day trip from Melbourne and you really need several days to fully appreciate it. I wasn't sure how you were getting back to Adelaide from your post but if you are driving, be aware it's a 10 hour drive from Melbourne on the major roads without any detours to see things.
Wineries a good option if the weather is not great (many day tours available) and the National Gallery of Victoria is great. There is also an excellent museum, zoo and botanical gardens that hold their own attraction in winter. Melbourne is full of restaurants, shops and bars to explore and is famous for its laneway culture.
Enjoy!

As a guide, cheapest advanced purchase airfares Canberra/ Melbourne for 5 June are currently about $110 (plus credit card fee); the Greyhound bus fare is half that, but the trip is 8 or 9 hours and mainly in the dark, compared with a flight of just over an hour.

I would certainly agree when telling you to do the GOR, such a fantastic and beautiful way to see some of our countries natural beauty. Stop in a small places such as Torquay, Appollo Bay and even down to see the fairy penguins..

Id recommend a flight from Canberra to Melbourne. You can pick them up cheap enough with Virgin Australia or Qantas. Its a quick flight and quite a scenic flight as you fly over some of the snowy mountain areas that time of year!

I would skip Brisbane also. IMO you are best of heading on a 3 hour flight from Sydney up to Cairns and visiting the reef, if you do then try and do a trip to the Low Isle. A beautiful catamaran out to a very small island and you head back home at sunset with a drink in hand listening to a guy on his guitar.. heaven!

In Sydney you must visit the Zoo, Bondi/Manly, Blue Mountains...so easy to get around. Depending what you and your son are into, you might be interested in doing the harbour bridge walk or the sky walk around centre point tower.

Take a look at booking.com for some great accommodation deals, usually you can book well in advance for a room with free cancellation and you dont have to pay the money until you arrive. Very handy!

Also, take a look at viator.com to check out what to do in each place you visit. You can select specific dates and go from there.

Have fun planning what sounds like a wonderful trip!!

Thanks everyone for your responses and advice. We may stay in Melbourne area longer to do more exploring, and forget going up north for warmer weather.

From what has been said we will fly from Canberra to Melbourne.

Thanks again.