trying to work out date of conception?

The date of your last period is day 1. You are technically not pregnant the first two weeks of your pregnancy weeks (when you miss your first period you are 4 weeks pregnant even though you have only been pregnant 2 weeks).

Based on the due date you provided, this is what an online conception calculator said:

First Day of Last Menstrual Period: October 13, 2011
Probable Date of Ovulation: October 27, 2011
Possible Dates of Conception: October 23 to October 31, 2011
Due Date: July 19, 2012 (40 weeks)

That does not match what you said when you had your last period. Were you told you are 13 weeks and 5 days based on an ultrasound or based on your last period?

Based on your last period, I get this:

First Day of Last Menstrual Period: September 23, 2011
Probable Date of Ovulation: October 7, 2011
Possible Dates of Conception: October 3 to October 11, 2011
Due Date: June 29, 2012 (40 weeks)

Either way, you did not get pregnant in September. You conceived in October.