9 weeks - Doppler heartbeat

So my doctors won't do an ultrasound unless your bleeding or having other symptoms of miscarriage or if your uterus is sizing differently than your expected due date. Today was our 1st appointment. I am exactly 9weeks. We couldn't find a heartbeat but midwife says it's the lower limit of when you can start finding it on Doppler. Still, no dating ultrasound was ordered. Have to go back in a week for another fetal heart check. Even though she says its normal, I can't stop from being nervous... Any similar stories? Would hate to be 10w pregnant and find an empty sac! I hate that they are so conservative about the daring ultrasound. :(