Eat more fat!

30g of fat is way too low, especially with <100g of carbs, too. That's a recipe for disaster in so many ways, not the least of which being micronutrient deprivation, which is exactly what we don't need (see also: rabbit starvation).

Also, consider more food in general. A 1200 calorie goal usually indicates that the person has set their weight loss goal to 2lb/week. That's generally too much for most people, especially if they're starting a new way of eating. Go with a more modest deficit, like 1lb/week, at least until you adjust to your way of eating, then slowly increase your deficit if you feel you can handle it.

You only need about 1g/lb of lean body weight in protein. Find out your body fat percentage and use that to find the amount of body fat you have, then subtract that number from your total weight. That's the upper end of your protein goal and you don't need to worry about trying to go over it (though it's a good idea to try to get close, especially if you work out a lot).

Fill the rest in with fat. Yes, this might mean close to or over 100g, and may mean more than 50% of your calories from fat, but that is not a bad thing.

Fats are crucial for hormone function, cell structure, neuron structure, and vitamin production and absorption. Do not fear dietary fat or cholesterol. And no, having high triglycerides or cholesterol is not a reason to avoid fat. In fact, it's a reason to eat more fat, because carb intake is what is directly correlated with triglyceride levels, not fat.

With PCOS, it's common to find deficiencies in Vitamins D and K2, especially. Both of these are fat-soluble vitamins, found largely in animal fats. Vitamin D produced by sun exposure also required cholesterol to turn the hormonal precursors into Vitamin D.

Also, saturated fat is not bad. In fact, it's very good. As are monounsaturated fats. The vast majority of the fat in our bodies is saturated or monounsaturated fat. It's what our body runs on when we run a caloric deficit and are burning body fat. There's no reason to avoid them in our diet. The only fat to completely avoid is artificial trans fats (hydrogenated oils), and to limit is Omega-6 heavy polyunsaturated fats (seed and nut oils). Moderate amounts of polyunsaturated fats are good, but should have as close to a 1 to 1 balance between Omega-3 and Omega-6, because that's the ratio needed to benefit from the anti-inflammatory properties of polyunsaturated fats.

For some more info on the history of the low-fat idea and on the benefits of LC/HF, check out Dr. Peter Attia's stuff:

https://player.vimeo.com/video/45485034
http://eatingacademy.com/how-low-carb-diet-reduced-my-risk-of-heart-disease