I would assume your doctor is dating the pregnancy by the first day (or assumed first day) of your last period, since that is what doctors are trained to do. That is when the GA (medical count of weeks of pregnancy) begins. If you are nervous, you could always run these questions by your doctor just to be sure of the terms she is using.
From the estimated due date of October 6, you would have conceived about a month later than the December 12 date you're asking about. That date also implies that you had a period between the guys, didn't you say that happened?