Hello,
My DH (he's a registered nurse) and I found our baby's heartbeat on our home doppler at just 11 weeks 2 days. IT depends on the doppler, where bubs is positioned, where the placenta is etc etc.... and also how experience the GP or whoever is at using the doppler! They aren't the easiest things to use but as baby gets bigger it's so much easier to find baby's heartbeat we find anyway....
you are still only 10wks so give it some time..... most dopplers don't detect until 12wks+

Good luck sure all is just fine not long til your scan.... and then you'll start feeling bubs move it's the best feeling!!

Hearing our baby's heartbeat is the most beautiful sound in the world..... it's the sweetest sound ever