A few things to keep in mind if you want to lose fat. First, if you want to keep the fat you lose off, you can't restrict your calories that severely. 1,300 Calories is downright starvation, and 1,500 Calories is borderline. To safely lose weight, you should only eat 250-500 Calories/day less than you burn. Given that you're a female who is at least moderately active, you probably need 2,000-2,400 Calories/day just to maintain your weight. The Harris-Benedict equation seems to work quite well for calculating this, available here: http://www.weightloss.com.au/weight-...calculator.htm

There are a lot of problems with severe Calorie restriction. One is the body's tendency to catabolize (eat) its muscle tissue when it detects starvation. This is because muscle mass is expensive to maintain in terms of energy; one pound of muscle consumes about 60 Calories/day. Don't want all that energy-chugging muscle around when one is barely eating. Remember, we didn't evolve from athletes with a secure food supply. We evolved from nomads who quite often were not entirely sure when they would eat their next meal.

Your goal is not weight loss. It is fat loss. Losing muscle is bad - not only because it makes you slower and weaker, but because muscle mass helps you lose fat. To lose weight, you want a high basal metabolic rate, not a low one. Also, it is difficult to eat all the vitamins and minerals you need to stay healthy while only eating 1,300 Calories/day or so.

Eat your egg yolks. I say this for a number of reasons:
1) They contain a lot of excellent nutrients;
2) They contain the beneficial fats of eggs (such as Omega-3), whereas the whites are only protein;
3) A lot of people don't eat egg yolks because they contain a lot of cholesterol (170-220mg/egg). However, cholesterol intake has next to nothing to do with cholesterol levels in your blood stream. Over 70% of the cholesterol in a typical omnivore's body is produced by his/her own liver. The three prime factors controlling your cholesterol levels are, in order of importance: physical activity, types and amounts of fats consumed (monounsaturated and polyunsaturated being good, saturated being bad in excess and trans being very bad in any amount), and genetics;
4) Since you are a vegetarian, you eat next to no cholesterol anyway. Cholesterol is used as a component of many vital organs, especially the skin and nerves, in animals, but not in plants;
5) Egg yolks taste pretty damn good IMO.

Dense vegetarian protein sources: cottage cheese (watch out for the sodium content of this, however; you shouldn't eat more than 2,400mg. of sodium per day), regular cheese, yogourt, fermented soy products, eggs, milk, nuts, kidney beans.

Protein shakes really aren't necessary, especially for a non-bodybuilding female, but if you really want to go that route, get a whey/casein mix. Whey is used by the body very quickly, whereas casein is digested much more slowly. This ensures that your body will have protein available as it needs it, rather than a sudden spike of protein and then nothing a couple hours later, as would be the case with a 100% protein mix.

Excellent choice staying away from processed soy products. The only good soy products are fermented ones, such as tempeh, miso, and fermented soy sauce. The problem with fermentation is that it takes time, and therefore money, so a lot of unscrupulous companies skip that part and try to sell us unfermented soy products as "health food." For about a billion reasons I won't get into here, unfermented soy products are very bad for one's health.

Don't be afraid of nuts because of their fat content. The fats you get from nuts are excellent. Peanuts and almonds (which are technically seeds, but treated as nuts) are also excellent sources of protein. They are very energy-dense, however, so you have to watch how many of them you eat.

Of caloric ratios: I find that a 50/20/30 carb/protein/fat diet works well for general use. That's what I eat. Bodybuilders would be better off on a 50/25/25 ratio, whereas some endurance athletes prefer 60/20/20 or even 60/15/25, presumably because of greater energy expenditure and muscle glycogen requirements. Anna Kournikova eats a diet of 60/15/25, by the way.

Note that I'm talking about caloric ratios, not mass ratios. If you calculated based on mass, you would eat more than twice as much fat as you intended, since fats have 9 Calories/g. and both proteins and carbs have only 4 Calories/g.

Stay away from refined grains and refined sugar. Foods such as white bread, white rice, white sugar, etc. cause huge postprandial blood sugar spikes followed quickly by huge insulin spikes, because the glucose in these unnaturally processed foods is so readily available. Insulin spikes not only tax the pancreas and can lead to diabetes, but they also cause the body to undergo anabolism - basically, the body's storage mode. The main function of insulin is to signal fat and muscle cells to store glucose in the bloodstream, which results in blood sugar levels dropping - the consequence being that the stored glucose in fat cells becomes fat. So eat whole wheat bread, brown rice, and use blackstrap molasses and/or honey as sweeteners if you need to (honey tastes a lot better than any other sweetener anyway).

Eat smaller meals more frequently. This will help keep your metabolism from dropping, will provide a more consistent supply of nutrients, and keep your body from being able to store large amounts of energy at any given time.

On a side note, I saw a magazine at the grocery store check-out today which exclaimed "LOSE 9lbs IN 5 DAYS!!!" Since it's impossible to lose 9lbs of fat in 5 days even if one were to eat nothing at all (barring third-degree burns or amputation) said "diet" no doubt accomplishes this mostly by muscle and water weight loss. Just goes to show how terrible popular diet plans are... there is a lot of money to be made in promising quick, easy results to people who don't understand biology. Proper dieting is really no more complicated than what I've described above, but it does take time and discipline. Keep it simple, eat cleanly, exercise a lot, and you'll succeed.