Could I just ask your exact reason for doing this? Not eating meat removes a lot of nutrients from your diet. Not to mention the foods you'll likely replace it with will make you gain weight, because I guarantee you you'll get sick and tired of 'healthy' vegetarian meals quickly.
I just hope you're not doing it to lose weight. Back when I was a fatty, I tried this same thing and failed miserably. Then I got my diet on (consisting largely of meats), started exercising, and lost all my weight. Eat lots of white meat like chicken and turkey (get them in the freezer bags) and lean red meat (92-95% lean), and your diet will be much more suited to losing weight.
If weight loss is your main goal, take this to the fitness section...I've been around there and although most guys are *******s, they do know what they're talking about and will give you a nutritious diet to lose weight.
Calorie in vs. calorie out, remember.
Also, the above user is right. Milk will give you all sort of simple carbs that will make it harder to lose weight. At least in large portions...I have nothing against milk.
Also, you need to distinguish sugars. Fruit is fine, it has natural sugars...just limit it to a few fruits a day. You want to avoid processed sugars, like the ones in candy. You seem to be trying to take in low carbs and low fat...don't be trying to just get your energy from protein.
Low fat diets are bull****, also. Just to throw that out there. Cutting carbs would do you a lot better. The whole idea of 'fat makes you fat' is ignorant. I'm coming off of a 2-month cutting cycle on a Ketogenic diet, which is a diet of only fat (roughly 160 grams a day) and protein (roughly 180 grams a day). Basically no carbs (under 30g daily which, as you said, means no fruit). I didn't have much weight to lose, but I was running it to lower bf% coupled with the weight training I've been doing for a little over a year, and it worked phenomenally.
They say the old woman's got the wisdom
'Cause she couldn't read the clock anymore
She said "The numbers don't represent the moments"
Says she don't see what all the ticking's for