No ultrasound at first visit? Not sure of dates.

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Hi,
First pregnancy and I'm a little confused as to why I won't be getting an ultrasound at my first prenatal visit. I have a slightly irregular cycle and am not exactly sure how far along I am (9wks vs. 10wks). Is this irresponsible of my doc?
I'm just feeling nervous about not knowing if everything looks alright in there. Will there be anyway for me to hear a heartbeat with no ultrasound? If not, how will I know lil' babe is doing well?
Thank you!