I personally wouldnt omit dairy unless you really think she has an allergy especially as she is veggie, it'll be an important protein and fat source. I'd want to know the doctors rationale for advising that.
I wouldn't say all kids have high carb diets, for example we don't eat pasta or only toast in the way of bread but we do eat some rice or potatoes at dinner. Could she have like scrambled egg for breakfast instead of porridge (do you have eggs as a veggie? Sorry for my ignorance!), maybe with veggie sausages and fried tomato/mushroom/beans. Or full fat yoghurt with fruit for brekkie.
It sounds like re-addressing the balance with the carb side of her diet would be a good place to start. Add more protein, whatever you use, tofu, quorn, cheese, beans. Give her plenty of fat, it'll lubricate her stomach.
You only have to think about you cook carbs, in a big pan of water usually or you add a jug of water to flour to make bread. It continues absorbing water in your stomach, like a sponge, that's why it's dehydrating.
Try upping her fluids with some soups, smoothies, homemade ice lollies, hot chocolate at bedtime, any sort of inventive way to make it interesting! Fruits and veggies are mostly water. You may already give her these things, it's just about balance.
Like for lunch, instead of sandwiches, give her 'kebabs', thread cubes of cheese with veggies onto skewers, hot ones with tofu, halloumi, veg or fruit salad ones - those would do well for lunch boxes too at school if cold. If she needs extra filler, add a small portion of rice salad.
Doctors know little more than you or I about nutrition as they just don't study it at med school.
I couldn't tell you why doctors don't suggest magnesium, maybe other more modern laxatives have taken over. But it's really safe, and magnesium is an essential mineral used by the body like calcium is. It's good for bone health, the brain, nerves - so some people use it as a health supplement too. Natural sources of magnesium are cocoa, beans, peanuts, any seeds like pumpkin, sesame or sunflowers, chickpeas, dark green veg - so eating any of these in abundance will help her go.