Congratulations on your PG! I'm so sorry to hear of your miscarriages. I had a miscarriage at 12 weeks and totally understand where you are coming from with regards to the stress you are feeling right now
With this pg I had kind of spotting which stressed me greatly but everything is going fine so far. Try and relax as much as you can. Stress is only going to make you feel worse. Please don't take this the wrong way, but I think we can talk ourselves into the worst case scenario an even talk ourselves into pains etc cos we are so worried about it.
With regards to the Doppler. It would probably be more of a stress at this early stage. Even midwives and Drs have difficulty finding the HB with a Doppler cos bub is still very small. Down the track if you are still anxious it may be worthwhile, but I wouldn't do it now.

Sending heaps of sticky vibes and calming vibes to you.