Is it okay to put children on a vegetarian diet once they are off the bottle?

Yes. Dr. Lonsdale has given you good advice. Strict vegans need to supplement and those who eat eggs / milk may need to as well. Get plenty of good protein. In the us, adventist children thrive on a mostly-vegetable diet, supplementing wisely. If junior finds being a vegetarian difficult as he/she grows up in a culture of meat-eating peers, it would seem reasonable to respect his/her wishes.
Maybe. I approach this with caution because it doesn't give me a snapshot of the parents experience with the vegetarian lifestyle. If you have lived in this lifestyle for years you are ware of the alternatives you add to the diet to balance the nutrition. I don't condone it in first generation new vegetarians who lack the type of family lore needed to balance the diet automatically. More knowledge-okay.
Yes. A plant based diet is O.K. As long as it contains first class protein obtained from nuts, seed and legumes. Dr esselstyn has a book entitled "preventing and reversing cardiovascular disease with a plant based diet".