It doesn't sound like you're the dad. A September 2 due date gives a December 10 conception date, a September 3 due date gives a December 11 conception date. Sperm only lasts about 5 or 6 days in the woman's body (if any escaped the condom).
I assume that you are aware doctors don't count "weeks pregnant" as beginning on the date of conception, but on the first day of the woman's last period? When her doctor told her 5 weeks 4 days on January 6, he was indicating she conceived around December 12.
Don't obsess over this "three days ahead" stuff. It sounds like you got the "three days ahead" notion from a later ultrasound, which is not as reliable for dating pregnancies as earlier ultrasounds. That is probably why the doctor didn't change her due date.
Although all embryos begin as one cell and then divide into two cells, then four, then 8, then 16, then 32, at a known pace, after a while some babies begin to grow more rapidly or more slowly compared to the average. This means that although a 7th-week ultrasound can be spot on, or off by only one day, by the time a woman is in her 40th week, the due-date estimate based on measurements from an ultrasound can be off by up to three weeks.
Also, 3 days doesn't move things back to the time when you had sex. Even if the baby had been due August 31, the conception date would have been December 8, not earlier. Your sperm would not have lasted that long from sex November 25, if any did escape the condom.
I am wondering if you want this baby to be yours. Is the other guy in the picture? If he is not, and you want to be, there is nothing to stop you from doing so. A lot of guys meet women with children and fall in love with them and take on the role of dad, and a lot of guys meet someone who is pregnant and do the same. If you are merely curious and wanting to be sure you are off the hook, it pretty much sounds like you are, though it is ALWAYS smart to do a DNA test just to confirm everything. But if you are kind of interested, don't let her having a child from someone else put a kibosh on things, unless, of course, she is with the baby's dad. :)
If you are now at the point where you're relieved by what I'm telling you and just want to put the whole question to rest and go on with your life, my suggestion is to go to a lab certified by the family courts in your area of jurisdiction and get a DNA test. It's not wildly expensive, and it is very worthwhile for the peace of mind. The clerk at the family court could tell you where to go. Don't use an at-home test you buy at the drugstore, their results are not admissible in court because of the possibility of mistakes or someone tampering with or switching the swabs. Go to a lab where everything is handled properly by the third-party (disinterested) techs, and ID is required, and so on. I don't think there is any question that this baby was conceived in December, but I do think you might be glad to have everything officially confirmed.
or the other guy is the father??