While exercise can contribute to the depletion of iron stores, its mostly a matter of getting enough replacement. You also have being female to add to the situation. Your body doesn't make iron, so you have to eat it. That is often at odds with trying to lose weight and eating less. You also want to optimize your absorption of the supplement by not taking it with food and making sure you take a vitamin C or orange juice with it.
I'd start off slow, just so you don't wear yourself out. Pay attention to your energy levels. However, there is no contraindication to do exercise with anemia, you may just not feel like doing it. I once met a lady with a hemoglobin of 1.9 that was functioning normally, she had just gotten used to it over the years.