I expect Chubby will be on the board soon to give you the real story but as you know June is the start of winter in Australia and I believe temps. range between 9 and 16°. Similar weather to what parts of the UK has been having this past couple of weeks. Not beach weather, though anything is possible. I think it rains mostly in Spring but I did get rained on a couple of times when I was there in February on one of my trips.. So I would say a lightweight rain jacket or brolly and a fleece.

Yes Judith has it some up the weather in Sydney at that time of year will be colder a jacket or jumper and jeans or slacks a light rain coat as there could be showers at night it will be colder about 8 to 10 c daytime about12 to 20 c
Our winters are no where as cold as yours the top part of Australia around Cains has its best weather at that part of year
Just hope the weather is kind to you you get the summer change of weather you can get at that time of year July August is the worst time