If you get an ultrasound they will ask the date of your last period and if it is close to that they will keep the date the same. Ultrasounds in early pregnancy can be off by 5 days either direction so it could say one thing one day and then a couple days layer completely change. That's why they usually will only date a pregnancy by ultrasound if you don't know the date of your last period.
The ultrasound will not base it on your last period. They will base it on the measurements they get when they measure the baby. The date of your last period has nothing to do with it unless you have a really regular cycle! If you know that you conceived on 5th december then i would estimate your due date to be 28th August. This is pretty close to what your doc said based on your last period so you must be pretty regular. The ultrasound might date you off by a day or 2 though. When i had mine i know the date that i conceived and when i had my first ultrasound i should have been 10 weeks 1 day but the measurements put me at 10 weeks 2 days. It can be off by a day or 2 anyway and dont forget that less than 5% of babies are actually born on their due date!
Good luck!
unless your baby is measuring differently the ultrasound will base it off your last period give or take a couple days, which won't really matter since due dates are estimations and baby is very rarely born on it.