As long as your fiance entered legally and you are a citizen, you should be able to adjust (Assuming no other issues - the question, as you note, is timing.
A marriage-based green card case normally takes five-six months from filing, though there is variation depending on where you are processing. So, cutting a bit close to actually get the green card by end of December assuming you file after the last week of August.
However, when you file for a green card you can also file for Employment Authorization and a Travel Document, which take about three months from filing to come through. These should be there in time to travel end of December (traveling without them abandons the adjustment case, and she won't be able to reenter on the unexpired F-1.once married and having filed the green card).
Speak to a lawyer for further guidance on your case; certain things, such as the prior J-1, should be fully evaluated.
I agree with the above answer.
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