Raymond,
There are actually two gondolas to reach the top of the Aguille du Midi, and the trip takes about 20 minutes or so. One important point to mention is that the Aguille is at 12K feet+ so if you've ever experienced any altitude related issues, that could be a problem.
It is possible to make the trip to Italy and back in a day, but unfortunately that won't be possible in your case. From the Aguille du Midi, you'd first have to take the Panoramic Mont Blanc across the glacier to Pointe Helbronner, and then the Monte Bianco down to the Courmayeur area. According to the current schedules, the last run of the season of the Panoramic Mont Blanc is 25 September, so it won't be operating in early October. You'll have to be satisfied with your trip to the Aguille du Midi.
I'd suggest adding at least a day in Chamonix as there are many other sightseeing options in the area. You could for example take the Montenvers Mer de Glace train and have a look at the glacier, do some Paragliding (as the participants of The Amazing Race did this season), do some hiking on the many trails in the area, etc. THIS website should provide some ideas.