Hi Sophie,
The only reason I could see that your doctor would want to do the endometrial biopsy is that she is looking for an explanation for your low hemoglobin level. Even though you have no sign of bleeding, your doctor thinks bleeding could be a possibility.
I don't have enough of your background to be certain, but if your Hb level has typically been around 9, then there is no reason to look for bleeding as an answer. If your Hb has suddenly dropped, then exploring a bit might make some sense, but ONLY after iron studies have been done. If your doctor wants to do an invasive biopsy before doing iron studies, it's time to get another doctor. All of your blood counts point to thal minor as the cause. Iron deficiency does remain a concurrent possibility but this cannot be assumed in thalassemia minor. An iron panel is necessary to diagnose iron deficiencies in thal minors. This is thal 101 and if your doctor can't bother to check out what I am saying, then you need a doctor that will recognize at least the very basics of thal minor.
Your vitamin D level is marginal. 30 is the lowest to be considered normal, but bumping it up would be a good idea. You have good habits that are keeping you more fit than would be expected for your Hb level, so do keep up the exercise. It does wonders for optimizing the oxygen level.