I did the Lukla-Namche distance in two very convenient days with a bigger group as a part of a trek to Kala Pattar. We were not in a hurry at all. We took our time to have our lunches on the terraces of tea-houses and even so we always arrived to our camp sites before 2 PM. If you arrive to Lukla with one of the early flights (around 7 AM), don't have a lot to carry and of course if you are in good shape it is definitely doable in one day. The question is more like, is it worth the rush. Will you be there to train or to take the time and look around? An other thing is, that after 2 PM the chance for some rain or snow becomes much higher.
For the Namche-Lukla leg, if you want to do the whole trip as a day hike, you must leave extremely early, because the flights to Kathmandu leave right after dropping off the incoming passangers and taking on the outgoing. (Sometimes they don't even stop one of the engines.) The last plane leaves before 10 AM, because the weather can become dangerous as the day progresses. Most people (us included) spend a night in Lukla to be surely there early enough.
To cut it short, it's almost impossible to do it in one day, it's possible to do it in two, but with questionable enjoyment factor, best option is to give it three days.
I can't help about the September/October weather, I was there in April.
The trek is safe and straightforward. It's hard to get lost even if you want to. I have seen trekkers alone and with personal guides also. With a small pack for max. three days I wouldn't hire a porter or a guide. (But I'm a man, ladies might feel differently.)