Hormones involved with Menstruation (FSH, LH, Estrogen, Progesterone, etc.) will vary depending in concentration depending on the time-frame:
You are correct in saying that not much blood is actually lost in the menstrual fluid: Less than 80mL (80cc), although the blood's origin is ultimately the circulatory system. Does it affect the quality of the blood? No. Usually not enough iron is lost during menstruation to make a difference between being able to donate blood and not donate. However, women who bleed heavier than the average can experience anemia (iron deficiency) - although anemia attributed to menstruation is often misdiagnosed gastrointestinal issues (up to 86% error rate).
One thing to consider is that common pain medications can affect blood content, and thus a woman taking aspirin cannot donate platelets for 5 days after she stops, and a woman taking NSAIDs (like Ibuprofen) cannot donate for 2 days after she stops.
...the combination of blood loss from periods and donation will make iron deficiency anaemia more likely, particularly if the periods are heavy or prolonged. This effect can be minimised by taking supplemental iron.
In general, as long as the woman feels well or the pain is controlled, she is perfectly capable of donating as long as her iron levels reach the minimums. The blood makeup is not significantly different, although hormone and iron levels will minimally fluctuate.
As always, this response is based upon information during some light research. I am not a doctor, and the information presented in this response may be modified later to increase accuracy or remove errors upon the discovery of new information.