Agree with @KirstenBlest Lots of 'normal' everyday foods are vegetarian.
And, although KB does not say this, lots of fake meat /ready meal products targeted at the vegetarian market taste awful and have a texture that is even worse. They're expensive and ultraprocessed too. Protein shakes come into the similar category - we do not need that much protein, and it's found in bread and milk and yoghurt and nuts and grains.....
My personal vegetarian dislike in many eating-out places is sweet potatoes with/in everything. Yes, they have their place but they are SWEET and I don't have a sweet tooth. One of the worst concoctions (to my taste) that I've seen - on the menu of a posh (well, expensive) restaurant - was a main-course 'sweet potato and apricot burger', served in a white bun.
As others have said, for a very quick snack, nothing wrong with peanut butter or hummus on toast (ideally serve with raw veg sticks/mini tomatoes ) or even good ol' Marmite on hot buttered toast. Or a little bowl of toasted seeds and nuts - easy to do in the overn - perhaps with a sprinkling of tamari soy sauce. Even Twiglets (wholemeal flour, relatively low nasties) might be possible as a very occasional instant something-to-munch.
@OP I know you say your daughter does not like eggs, but will she eat them hidden in home-made pancakes? As you know, these are almost instant to make and very nutritious, and can be served with all kinds of vegetarian things, from simple lemon juice and a scattering of sugar to fresh fruit (or high-fruit jam) with cream or yoghurt or butter, or with something savoury such a thinly-sliced cheese. I like little pancakes topped with home-made hummus and grated carrot or with aubergine, garlic, parsley and yoghurt dip (a more 'grown up' flavour, perhaps). Large, thin pancakes can be used instead of wraps.
More 'hidden' eggs: some cakes - eg brownies/blondies and Nigella's chocolate olive oil cake - have a fairly high egg content, and contain very nutritious nuts as well. You can also hide eggs in fritters- eg sweetcorn or courgette.