We went at the end of September with our dog. Al books all recommend taking the gondola up part way but unfortunately for us they were all shut for repairs prior to the ski season so we walked from our hotel! It took us about 7 hrs in total to talk from chamonix town and back again. There is a national park that you have to walk through which says no dogs but we put her on the lead and snuck her through as after 3 1/2 hrs we didn't want to turn back with only a few miles to go!!
Once at the top the views are just amazing and even 'out of season' there were still lots of people having picnics and enjoying the scenery.
One MUST DO on this walk if you're heading back to chamonix is stop off at La Floria (it's well sign posted) for a drink and soak up some sunshine and views. It's truly a stunning little cafe.