A human can adjust to a low hemoglobin, and in your case it may cause a higher HR. I had a hemoglobin problem about 20 years ago and didn't go to the doctor until my skin turning "yellow", I am a Caucasian. The routine blood test showed a hemoglobin of about 6. My doctor said that was low enough there was a possibility that I could pass out. I got a blood transfusion and underwent a number of tests. The only problem that was identified was I was Iron anemic. I too an iron supplement, and the anemia was cured and the hemoglobin came up to 13+ over the next several months. I no longer take an iron supplement, and I have not had any more low hemo problems... I don't know what the problem was.
Well i have this diseasesince 10 years. Before that i was very very fit and no HR issues.
The HR is not a danger as I see it. The low hemoglobin should be treated and if you can get it up another 30% or so you may find a lowering of the HR, I am not sure about that.
What was your past normal HR, at rest and at light exercise?