10 weeks for 1st appointment

Found out I am pregnant almost at week 4 yesterday after 10 months of trying! I called my doctor to schedule my first appointment, hoping it would be 6-8 weeks mark. Well my doctor won’t see me before 8 weeks, which I hear is normal. But she is out of town for weeks 8 and 9, so she can’t see me until week 10! This makes me so nervous just not knowing if there will be a heartbeat for the next 6 weeks. Am I over reacting? Should I be nervous waiting that long? Or is it normal to wait 10 weeks for first appointment?