We are vegetarians, and we feed our 17-month-old son everything we eat now. When he was in the age range that you are inquiring about, we fed him lots of black beans, black-eyed peas, and other beans that we bought in bulk and cooked and froze ahead of time. He just picked them up on his own and ate them. He also loved refried beans. As time went on, he wanted more flavor and so we started just giving him our food and stopped feeding him plain beans.
He has only had eggs a few times because he didn't care for them, and we don't purchase them, but I'm thinking scrambled or in an omelet would be good. It would definitely be easy to eat without causing a choking hazard.
A great book is Vive le Vegan (even for lacto-ova vegetarians). She has a lot of recipies and a feeding chart that teaches what foods to introduce at what ages. The rest of the book is a cookbook, but I found her section on babies and children so helpful.
I applaud you for raising your daughter vegetarian!
Oh- I just thought of something - tofu. Our son loves that. It's a perfect food for infants because it's so easy to chew.