Doppler monitors (or fetal heart monitors) appear to be safe for the fetus.
However, they are generally not recommended for home use. In many cases, they cause huge stress for mums to be as opposed to delivering them relief and peace of mind.
It can often be tricky to find the fetus' heart beat since the fetus moves around a lot. Also, the fetal heart beat has variation to it and mums to be frequently get very concerned when the heart rate is higher or lower than they have experienced before.
Best bet is to leave it to the doctor's surgery where you can enjoy it best.