http://www.ifyouski.com/resorts/country/australia/

http://www.ifyouski.com/Resorts/View/?objectid=218004

You'd be looking at skiing in the southern hemisphere, at this time of the year. Have a look at the link which will also give you an over view of other resorts.

Or go to one of the European resorts where you can do year round skiing on a glacier. For example, it is possible to stay in Mayerhofen in the Austrian Tyrol and ski in the height of summer on the Hintertux glacier though conditions won't necessarily be best suited to beginners.

The same could well apply to southern hemisphere resorts too at that time of year because you're coming towards the end of their winter season. Going skiing in the southern hemisphere in September is like going in March/April in the north - the best conditions are probably gone.

SM

Queenstown or Wanaka in South Island New Zealand are great ski-ing destinations but as the previous poster said it's towards the end of the season so conditions may be not so good, though spring ski-ing can often be great.