Term babies are born with all the iron they need for around the first 12 months. Ideally the cord should be left to stop pulsating before it is cut because this allows the baby's blood to transfer back into his body properly, ensuring that those iron stores are tip top. Premature babies - usually those born 4 weeks or more early - may need more vitamin/iron support earlier because the mother transfers a lot of the stores to her baby in the last 3-4 weeks of the pregnancy. In this case parents should be given additional support and advice by a paediatrician.
Breast milk doesn't contain all the iron and zinc that a baby needs to thrive because the baby's stores are there to cover this - but what is there is in a form which is highly bio-available. Formula has far more, but it's less easily absorbed and because there's so much iron it can even trigger micro-bleeding in the bowel which can lead to anaemia in extreme (rare) cases, ironically.
Between 6 and 12 months the baby's iron store starts to run down, and while he's being supported by all that lovely bio-available iron in BM, he will START to need a little more. As he learns to eat he'll be getting plenty of iron from food if he's given the right things. Meat is the easiest source. A baby-led weaned baby will suck and gum on a piece of meat and suck out all the juices which will give him everything he needs. Given this about 3 times a week he doesn't NEED anything else really if he's given full access to the breast - although of course you will be introducing other foods too, teaching him about flavours, textures, colours and social skills at the family table (or at least how much fun it is to throw food at the wall/his brother/the dog - or is that just my house?).
Iron is also in most breakfast cereals - added in with vitamins as well - so if you're giving cornflakes or rice crispies, say, he'll be getting vits and minerals here. As long as you're introducing lots of foods and he's getting either formula or breastmilk, all will be well.
One final one to consider is Vit D. Some people are a bit low - easpecially if they don't get outdoors much, or cover for cultural reasons, or just because they live somewhere pretty north. Vit D drops can be offered for your baby if you feel you're at risk of low Vit D.
I highly recommend Gabrielle Palmer's Complentary Feeding book for the latest research into all this!