You are definitely going to go through considerable water. Electrolyte (sodium/potassium) balance might be a challenge if you're sweating a lot. Most of us consume too much sodium already, so it's probably the potassium you'll need. Bananas are high in potassium. There are some other good natural sources that you can look up. And if you do need the sodium, just bring salted nuts with you. Nuts and berries are good energy sources for the trail and don't take up much space.
Because you'll be burning a lot of calories, don't be afraid of eating higher fat foods (fats are 9 calories/gram vs 4 cal/gram for protein or carbohydrates). Mmm, avocados! Eat 'em up!
Stay away from simple sugars in your foods - they'll make you crash (like white bread, candy bars etc). Complex carbohydrates allow a slower steadier energy release.
Being vegetarian isn't as great a challenge as being vegan so adequate protein will be easy (an egg or two a day plus some other sources like corn and beans, or soybeans and rice, and you're good to go).
And of course, you'll need a cold beer and massage at the end of each day