Something I've found since Small came along is that just visiting a vegetarian restaurant doesn't mean that little vegans will be catered for. I've encountered all kinds of attitudes - from well thought out kids menus, those willing to make something to places who make it plain they don't like children being there!
At the beginning until as long as I felt I could get away with it I'd take her food with us. Most places don't mind this, especially if you are still in the 'baby food' weaning stage but now she's 15 months it's harder to get away with.
I guess our 'local' vegetarian place (it's still over 30 miles away!) The Warehouse Cafe in Birmingham do a pretty good job. We always take our own booster seat when we eat out as most places don 't have a highchair, but happily they now have one. They'll make smaller portions of adult meals for kids, but sadly they got rid of their kids menu a while ago and adult food isn't always suitable for toddlers so we really have to pick & choose what she eats there. They're pretty happy to try and help with any requests though and are generally a helpful lot.
I was really pleased to see a kid's menu with vegan options at both places in Lyme Regis we visited last week (Aroma Cafe and Tierra Kitchen). When you have kids eating out has to be a good experience for the whole family. It's little details such as child friendly plates and cutlery which would make the experience so much better.
Where do you eat out with your kids? I'd love to hear others experiences on this!