How long after turning vegetarian might iron deficiency anemia start to show up?

Not necessary: Contrary to what you might have heard on tv or some "experts", you don't necessarily get iron deficient just because you're vegetarian. Lots of vegetables, beans, & fortified bread are loaded with iron. Many cultures survived millennia on little to no meat & many others with almost no red meat. It depends on the variety of your diet & medical conditions present. Plus there's iron in eggs & fish.

Hopefully never: Humans have no way of getting iron out of our systems except blood loss; we regulate iron by how much we absorb in our small bowel. If someone is not losing a significant amount of blood (we all lose a little) legumes, broccoli and kale should enable a vegetarian to remain adequately iron saturated. We absorb iron slowly, but store it very well, allowing most to go years even without fe absorption.