I had this same worry. I think it's a normal fear that we have less time that we think. But when I went for my first ultrasound d were were pretty much right on track. The dating only bumped me forward 4 days. Try not to worry too much about it!
I would say the chances are pretty slim. But when you go to your first dr appt, if they do a vaginal ultrasound, they will measure the baby and compare the size the measure to the date of your last period.