In Canada the normal range for a female is 120-160 g/L. In the US, the range is 12.0-16.0g/L. Perhaps you are in a country that uses the same range as Canada?
I relate very much to your questions, as I have had the very same drop in my hemoglobin, but over the last year. I was at 13.5 (135 according to the scale you are using) last March, and since then have dropped to 12.2 (120). I have had multiple physicians assure me that this is not an issue, and my fears are mostly assauged, but I do occasionally still worry about it, especially since I have dizziness.
Have your red blood cells dropped as well? Mine went from 4.5 to 4 in the same period of time. My platelets had been down a bit in the summer, but have now risen back up to the level they used to be at.
How are your iron levels, as in stored iron? RBC and hemoglobin reflect circulating iron; you can also have STORED iron tested. If your stored iron is low, then perhaps you have iron deficiency anemia. In that case, ask your doctor what they recommend. Iron deficiency anemia is very common for menstruating women.
Part of my concern was the fact that my stored iron, ferritin and b12 are very much in the normal range, while my RBC and hemoglobin have dropped a bit. But really, not a HUGE amount. If it weren't for the dizziness, which causes me to start looking for answers to why I don't feel better, I would not be worried, I don't think.
Perhaps you should go back to doc and get to the bottom of whether you have iron deficiency anemia (that could be the cause of the hemoglobin drop).
Anemia can also be caused by chronic disease, but in this case the distinguishing factor is low levels of CIRCULATING iron, as in, RBCs and hemoglobin, and stored iron that is normal.
I am NOT a doc, so please take my response with a grain of salt and talk with your doc. And if I have gotten any of the these details wrong, I apologize; all of this simply stems from my own research as a result of my own situation.