Is it safe to eat a vegetarian diet in pregnancy?

Yes. A vegetarian diet is perfectly acceptable in pregnancy. You should monitor your diet to make sure you are getting enough protein from other sources like beans, eggs, diary products and nuts. As with nonvegetarians you should take a daily prenatal vitamin and a calcium supplement.
Yes, and. You will still need prenatal vitamins. If you are vegan (not eating eggs or dairy products) you'll also need B12 for sure.