Lets take a look at some of the areas you should be concerned about if you are raising a vegetarian child:
Energy: Small children need lots of nutrient-dense foods 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 as much of a concern. If you wish to raise your child as a vegan (one who eats no animal products), it may be best to wait until your child is older and his gastrointestinal capacity is greater.
Protein: If you are eliminating only meat products from the diet, then protein is easily replaced by eggs and dairy products. However, with no animal foods, 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, lack of calories, not lack of protein, has been the causal factor in vegan children with growth delays.
Vitamin B12: B12 is found only in animal products, or as a contaminant on some vegetable products, and vegans are at risk for a B12 deficiency. Especially at risk are babies whose nursing moms are marginally deficient in B12 when, even if the baby isn't weaned to be a vegetarian, he may be suffer from the consequences of his mom's deficiency.
B12 can be added to the diet through fortified soy or nut milks.
Vitamin D: is especially lacking in vegan diets, where no fortified milk products are included. If you live in an area where you can get a relatively good amount of sunlight several times a week, a deficiency should not be a problem. Otherwise, try fortified soy or nut milks.
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, possibly offsetting the problem. For babies, an iron fortified cereal is recommended for at the first two years.
Calcium: For children on a lacto-ovo vegetarian diet, calcium intake may actually be very high due to the dependence on dairy products for calories and protein. The diets of vegan vegetarian children, on the other hand, have been found to meet only 40 percent of a child's calcium needs. Therefore, calcium should be taken in the form of supplements or in fortified soy milks.