How much iron should a child vegetarian consume per day?

As much as non-vegetarians. :)

This page from the Vegetarian Society will tell you exact milligrams per day requirements for people of various ages: http://www.vegsoc.org/info/iron.html#requ

The same page also says that chick peas and spinach are good sources of iron, and that vegetarians are no more likely to be anaemic.

It's really important to get enough vitamin C as it helps with non-meaty iron absorption. Daily vitamin B12 is also really important, and if you're feeling weak it really helps to take it regularly. I don't know, but I am a vegetarian and I eat lots of nuts and tofu. I think soy products will help too.