Like many runners, I’ve struggled with low iron for years. Surprisingly, since I stopped eating meat my ferratin levels have doubled and my hemoglobin levels have skyrocketed. That seems strange (and maybe even "iron"ic?), but I think because I ate meat so infrequently, it didn’t really help me much. (And even when I was only eating fish but having it 2-3 times a week, my levels were still only marginal.)
By dropping it completely, it forced me to pay more attention to taking in iron-rich foods every day and making sure I had something with Vitamin C at the same time to increase the absorption. I still take an iron supplement, but a lower dosage and less frequently. It’s amazing how much energy I now have to put into (and be used up by!) training. Since I don't want to eat meat at all, let alone a lot of it, I'm happy this seems to work for me.
It was also comforting to read in D. Enette Larson-Meyer’s book Vegetarian Sports Nutrition that it is almost impossible, even as a vegetarian, to not get enough protein if you are getting enough calories. She says that you would have to be very restrictive in your food choices to not get enough (for example not eating other protein-rich foods like legumes or soy products).