I found the heartbeat consistently from 9 weeks on, but it's very normal not to hear it until weeks later. I may have been lucky for a few reasons: 1) I used to work in L&D, so have lots of experience using dopplers and finding the heartbeat at various stages, and 2) I'm fairly slim (or at least I was until a few weeks ago).
If you do decide to rent a doppler, I would suggest trying it when you have an appointment or ultrasound booked. My doctor picked it up with his doppler a few days before I was able to. When I tried at home after my appointment, I was disappointed but not stressed because I had just heard my bubs and knew that it was my technique and/or the doppler that was the problem. I had an ultrasound a few days later, and so I tried it again and SUCCESS! Once I found it, I was able to find it every time after that.
Good luck! Using the doppler has been an amazing experience for me. Every time I started to feel panicky or stressed, I could stop it there just by listening to my baby. I listened to it fairly regularly until I started to feel movements, and it's been one of the most beautiful parts of my pregnancy so far.