In reply to TaxusBaccata:
Some thoughts:
Do you speak Italian? There won't be many English native speaking climbers hanging out in the Italian Alps. Chamonix is the best place to find partners.
On average, September is still summer season, then it gets into autumn and winter.
Alpine climbing is much more serious in autumn and winter and no place for a beginner.
On the other hand, you can do sport and trad down on the valley crags or further south in Italy until well into autumn and indeed over winter if you go south.
It will be a great opportunity to learn to ski or get better if you ski already, but the ski season won't start till December.