11 weeks, got one off ebay - angelsounds I think it was - don't get sucked into paying for the doppler gel though, baby oil (or vegetable oil if you are desperate ) work just as well

However I found I had to place the doppler much lower than I though to pick up the HB, eg right above the pelvic bone - they certainly aren't as sensitive as the ones OBs/Midwives use, and listen to your own heartbeat first, then search for a HB about double the pace, sounds like galloping horses, the swooshy pulsating sound is usually the placenta/umbilical cord I think
I got my angelsounds one off ebay as well. I was a surgical vet nurse at the time so I bought some ultrasound gel cheap through the clinic, lol. I also found that the heartbeat was much lower than I thought it would be early on. I almost had to point in down behind my pubic bone to begin with.

First pregnancy I found DS's heartbeat at 9 weeks. It took quite some time to find, and was faint, but once we found it we recorded it and it was magical.
Second pregnancy we couldn't find DD's heartbeat until 10 1/2 weeks. Of course I was getting a little nervous having found it earlier with DS, but all was fine
Third pregnancy we found DD's heartbeat at 10 weeks. Just as magical third time around ♥

I found that in the early days the doppler was amazing at calming my anxiety. Before DS we lost a bub so I was rather nervous in subsequent pregnancies. Before I was able to feel the babies moving around I found that listening to those amazing heartbeats even just for 30 seconds was enough to calm my nerves and reassure me that my baby was still alive. It also helped later in the pregnancy when I would have a period when a baby wouldn't move for some time, so I would just do a quick check to make sure they were just having a little snooze