What supplements should a vegetarian woman be taking?

Vitamin B12. It isn’t found outside of animal protein.

D3 – now for everyone, particularly in Northern climates during short days. Read Dr. John Fuhrman’S EAT TO LIVE, for advice on non-animal proteins.

Just Vegetarian? Or Vegan?

just vegetarian. I eat dairy.. Cheese, eggs once in a while, milk sometimes, ice cream (too much)

Is it different for men and women (I mean, besides basic dietary stuff like women need more iron)?

I don’t really know.. just threw that ‘woman’ thing in there in case anyone else knew

Iron.
Especially for women.
First, women need more of it (especially when pregnant, it allows oxygen to get to the baby). I can’t remember why for sure, I think its because of the blood loss during the cycle.
Second, its contained in red meat.
Third, it’s estimated that nearly 80% of the world’s population is iron deficient, and 20% is anemic. Check it. Look especially at “Who may need extra iron to prevent a deficiency?”