W.T.
I am raising my children vegetarian. If done wisely, it can be an excellent choice. Both of my boys are at the top of the growth charts with no visits to doctors for illnesses (not attributing the diet to that, just pointing out that it is conducive to a healthy lifestyle).
Number one is to make sure your children are getting a balanced diet. Protein, calcium, iron, etc....a good multivitamin in conjunction with healthy foods can help if you are concerned.
Protein seems to be a concern for a lot of new or non-vegetarians, but it can be found in lots of places. It is recommended that your toddler (don't know how old your child is) get about 16 grams of protein. People associate meat with protein, but it is in tofu, nuts, legumes, all dairy products (yogurt, milks, cheeses), eggs, etc.
Here is a good link for foods high in protein, iron, and calcium:
http://www.wholesometoddlerfood.com/toddlercalcium.htm
Although we are vegetarian, I do give (and take because I am nursing) a good fish oil supplement because its such a good way to get omega and dha oils....there are other vegetarian options though.
Expect some pushback from others. "Meat eaters" get a little defensive around vegetarians I've found! :)
Good luck!
I think most importantly, feed whole foods that are varied. Good for you