I really wouldn't advise getting too reliant on a home Doppler but you probably know this already! A midwife tried to find the heartbeat of my first baby at 11 weeks and couldn't so I would leave it a while longer before you try - I ended up freaking out when she couldn't find it (and at my 12 weeks scan they said she had been stupid to try so early) and I wouldn't want that to happen to you.
midwives don't check until the 16 week appt because it is difficult to find much earlier.
home dopplers really aren't recommended. they can create a false sense of security (you might be listening to your own heartbeat or the placenta, if you hear the babies heartbeat you have no way of knowing whether this is healthy or not) and can cause unnecessary panic if you don't hear anything.
I think the reason they are not advised is they can cause false panic.. but also false reassurance. Some people have apparently heard the heartbeat via the Doppler and been reassured whereas actually(we are talking later on in pregnancy) it's the movements that are the thing to monitor.
They actually have it printed in my annetenatal notes not to use a home dopler for the reason that as untrained professionals we won't know if we are actually listening to the heartbeat and even hearing the heart is not guarantee that it's healthy. They also don't tend to try listening to the heartbeat until 16 weeks because it can be harder to hear it before then. When I first heard the heartbeat at 16 weeks, I asked how they can tell the difference between the pulse of the placenta and the heartbeat and their answer was years if experience. Personally I didn't use one as it would have given me something else to get anxious about
I found my third baby's heartbeat with the doppler at 9 weeks. But it took a very long time and was pretty stressful in later weeks when I failed to find it again.
I understand why they're not recommended and can create a lot of stress, panic, or reassure you when you shouldn't be reassured, but I still think they can be helpful if not overused. I'm now 18 weeks and not feeling much in the way of movement or other pregnancy symptoms so it's helpful to have it to check every now and again.