Steve
I think deciding between September and October is really splitting hairs. Really, the weather is perfect for golf. Dave Elvins comments about the wind is appropriate. And Melbourne does have a 'wet' spring. But it is not what people from the east coast of the USA would call wet. It is mild, showers (generally) rather than rain. At worst, Melbourne spring weather can be like a Scottish summers day.
Hot in summer - yes it can be but on average we are talking about perhaps one or two days a month. The average summer maximum is about 80, although there is the chance of an occasional 100 day, albeit with dry heat.
The saying about melbourne weather is that if you don't like it, just wait a while. It will change. It is well suited to producing and playing great golf courses.
James B