Do you meet people every day (Nov-Jan)? Is it safe to camp in the wild? Have you met other woman doing it alone?
Yes to all of those. But Nov and early Dec is early season, and you will meet fewer people then, maybe barely anyone in early Nov. Come January there will be lots.
If you camp and make your own food
If? You will do this by necessity I suggest. In fact lodgings at convenient intervals have increasingly popped up in recent times, so you do hardly need to camp on the main central section these days. But in the far south, this is not true. It will cost you similar if you were doing the same thing in another typical developed country like France or Italy.
How long did you take?
Look at some travelogues at crazyguyonabike to get a variety of experiences. Be aware that if you are looking at older travelogues, more of it has been paved in recent times. You talk about "The" carreterra Austral but are you including the northern and southern extensions, adn there are some options here and there - I'd particularly recommend to go via P Ibanez, ferry to Chile Chico, and then along the lake, which is amazingly scenic, but also hard. So what you want to do?
Is the road in terrible condition?
You need to find someone who rode it yesterday to know that, since they might have might have done some maintenance last week, you never can tell. But you know extended sections are paved now, especially the central section which is all, or nearly all, paved, all the way to VCC and P Ibanez. Some of the far northern sections north of Chaiten can be very rough, but maybe someone has done something about that. But from Villa Cerro Castillo southwards it is typically very rough.
Should I bring a bike or buy one there?
You can now get high quality touring equipment in Santiago - not widely, only at one or two specialists - including the high quality steel luggage racks and panniers that are necessary if you do the really rough sections down in the far south. But it would probably be cheaper/easier/more choice to buy them somewhere else. But don't think you can get something suitable in P Montt.