In Melbourne in June and July, you can expect daytime temperatures around 55* F, more or less. Once in awhile you'll get lucky and get a nice sunny day pushing 70. If the wind is out of the north, generally you may get a pleasant sunny day with cold nights, sort of like a desert climate. If the wind blows out of the south, you might get something resembling Scotland. I found that a 55 degree day there feels colder than a 55 degree day in the US, mainly due to the wind. It really had a bite to it.
You may want to go earlier rather than later... the 7 years I spent there, it seemed as if it rained more as you got later into the cold season. August and September seemed like the dreariest months to me.
I played Commonwealth in early July one year and I found it still to be rock hard. To this day they still might be the slickest greens I've ever seen.
There has been, and still is in most places, a rather bad drought which has been occurring for years (hence the fires) and pretty much everywhere you go there are stiff water usage restrictions in place. So most clubs will only water the bare minimum (tees, greens, approach areas, clubs with higher budgets may water fairways sparingly).
I've never been to Tasmania but everyone says it is absolutely freezing that time of year. Of course, the locals generally grab the gloves and scarves the moment the temperature drops under 60, so it's all relative.