I had an ultrasound at 5 weeks 3 days and they couldnt see it or pick it up. I had another one at 6 weeks 6 days and they picked it up.... just.
The doc told me they can usually start to pick it up around 7 weeks give or take a couple of days but thats with an ultrasound not a dopler...i've hear some of those doplers you buy for home use can be quite difficult to find the beat so just beware of the shonky ones

Hope it helps