Lets take a look at some of the areas you should be concerned about if you are raising a vegetarian child:
Small children need lots of nutrient dense foods to meet their demands for growth and energy. Sometimes a vegetarian diet is so bulky that a child can't eat enough to get the calories he needs, and babies and toddlers need calories. The most dangerous time is during the weaning stage, when a baby is switching from high fat, high calorie mother's milk, to a less calorically dense diet. If some animal products are allowed in baby's diet, such as eggs and dairy products (known as a lacto-ovo vegetarian) then energy intake is not so much of a problem. If you wish to raise your child as a vegan vegetarian (one who eats no animal products) it may be best to transition to that type of a diet when your child is older and his gastrointestinal capacity is greater.
Protein: If you are eliminating only meat products from the diet, then the protein from the meat is easily replaced by eating eggs and dairy products. However, if no animal foods are eaten, it will be almost impossible for your baby to get the protein he needs. Eating complimentary proteins by strategically combining vegetable sources can supply high quality protein, even if not eaten at the same meal, yet the volume of food a baby would have to consume to get the proper amount may be difficult. Even so, not lack of protein, but lack of calories has been the causal factor in growth delays found in vegan children.
Vitamin B12: B12 is found only in animal products, or as a contaminant on some vegetable products. The vegan population is at risk for a B12 deficiency. Particularly at risk are babies whose nursing moms are marginally deficient in B12. Therefore, even if a baby hasn't weaned to a vegetarian diet, he may be suffering from the consequences of the vegetarian diet of him mom. B12 can be added to the diet through the use of fortified soy or nut milks
Vitamin D: It is especially low in vegan diets, where no fortified milk products are included. If you live in a area where you can get a relatively good amount of sunlight several times a week, then a vitamin D deficiency should not be a problem.
Iron: The iron content of a vegetarian diet may be high, but the iron is in the non-heme form and so is harder for the body to absorb. However, vegetarian diets also tend to be high in vitamin C which increases the absorption of iron many fold. Therefore the problem may be offset. It seems that the iron status for vegetarians is no different than for the meat eating population. For babies, including an iron fortified cereal is recommended for at the first two years.
Calcium: Actually, for children on a lacto-ovo vegetarian diet, calcium intake may be very high, due to their dependency on dairy products for calories and protein. Diets of vegan vegetarian children have been found to meet only 40 percent of a child's calcium needs. Therefore, supplemental calcium should be added, in fortified soy milks, or supplements.