Change of due date.

So I went to the doctor for my first appointment. Everything went well. Based on the date of conception I estimated I was 9 weeks give or take 2-3 days. The doctor told me based on my last cycle I should be 9+5. I'm only measuring 7+3. I'm like 99% sure of the date the baby was conceived. Is it possible the date they gave me is wrong? How accurate is the first ultrasound as far as measurements/dates go? This is my first and I know it's not as important as other things but if the new due date is right I will only have 2-3 weeks to spend with my baby before I start work again 😥. The thought makes me so sad.