Starving and miserable

1200 sounds way too low! I would talk with your doctor again, letting him/her know how you are feeling.
What is a normal day for you? Are you filling up on veggies? Drinking enough water? Good Luck on your journey!

Is your Dr a generalist that got their normal 1 class on nutrition, and hasn't made it their speciality?
Since every fast-weight loss method says 1200 too, it may not be very specific.
Throwing in low carb sounds like he's just willing to jump on diet bandwagon - or do you have actual pre-diabetes or blood sugar issues?

Then you should seek out a refer to a specialists - dietician in the US is their degree.
And even then some don't keep up with current info and studies.

While that is minimum daily recommended for average sedentary female - are you sedentary?

On MFP when you do more like exercise, you are expected to eat more.
Life lesson right there for weight management.
Along with when you do less you eat less. (that's how most gain the weight)
If you were and plan on exercising, then 1200 doesn't sound like it took that into account.

You do sound like you have a fair bit to lose - 2 lbs weekly might be reasonable if your body isn't under any other stress, until you have under 50 lbs to lose.

Then the rate should be slowed down to 1 3/4 weekly until 30 left.
1 lb until 15 left
1/2 lb to the end.

How active is your lifestyle outside of exercise - you may not be sedentary anyway if you have say kids/pets and household responsibilities - even if you have 9 hr desk job/commute time.
In which case 1200 was not taking that into account.

You also could be selecting foods that are not filing for your body, and some adjustment would be in order.
Though if it's leaving you tired that is body's first response to getting less calories than it's willing to deal with - slow you down.

That also could kick off or highlight a thyroid problem, results of which are making a person feel tired.

You also could be trying to play logging of food safe in your mind, and inflating the calories eaten, so actually eating even less than 1200.

well.... uh hum.... Most M.D.'s know dick about nutrition and weight loss. They only care about results and most don't care about long term results. When I was in the E.R. dealing with starvation issues, one told me he hands out 12-1600 calorie diets like they are candy. Yes, you are tired! That is the bodies way of saving energy when in a low calorie availability state. People spontaneously move less. NEAT levels dropping are well documented in weight loss studies. My suggestion is to find a WOE and calorie amount that you can maintain in the long run. Let your lifestyle decide your weight. Use the calorie suggestion from MFP, weigh and measure your food if you go that route, and find foods AKA a WOE that fills you up and keeps you satiated. I like the idea of "ideal" weight. It might not be our goal, we might not be as lean as we like, but its a place you are healthier, feel good, and can sustain. Cheers!

Has your doctor specifically told you that it's urgent for you to lose weight very, very fast, because of some critical health condition that your weight is aggravating? Is your doctor seeing you regularly while you diet (every week or few, for example) to do blood tests or otherwise check that you're OK nutritionally and physically?

If the answer to those 2 things are both "no", then you probably can increase your calorie goal. (Still check with your doctor!)

It's fairly common for doctors to tell people (especially women) to eat 1200 calories daily because that's old-school generic advice, most doctors don't have much nutritional training, and they assume that most people will not comply with the 1200 (maybe just because they estimate inaccurately, which is ultra common). If you are estimating your calories very carefully, and you're certain you're at 1200, that's a different scenario.

If you answered "no" to both questions at the beginning, then I'd suggest you set up your MFP profile and see how many calories it would suggest for you. Unless you have urgent health problems related to weight, you don't need to select "2 pounds a week", you can go slower to make it easier. Many people set themselves as "sedentary/not very active", but many/most women with jobs, kids & home chores are at least lightly active.

See what MFP recommends, then ask your doctor: "I want to eat XYZ calories instead of 1200, with a goal of losing ABC pounds a week. If I don't lose doing that for a few weeks, I will adjust my calories downward. Is there any reason I should not do that?"

I'd also point out that (1) the first couple of weeks of a new routine can be the hardest, and (2) many people find that focusing on nutritious eating (protein, healthy fats, plenty of veggies/fruits) helps them feel fuller, and perhaps even more energetic.

However, weakness and fatigue are really bad signs. Unless it's urgent that you lose weight fast, IMO, continuing would be risky. It's a myth that all women need to eat 1200 calories to lose weight: Some do, many don't. Those who do are usually some combination of petite, older, inactive, or the like. (I'm not petite, but average height (5'5"), older, hypothyroid, and sedentary outside of the exercise I log separately and eat back - even at age 59-60, 1200 was too low for me; I lost at a good, steady rate on more).

This is a good general article:

https://www.aworkoutroutine.com/1200-calorie-diet/

Unless you have a medical reason for:

A.) Getting the weight off ASAP
B.) An extremely low carb diet

Neither of these are necessary. I'm guessing your doctor is uninformed, or just lazy.

A.) Enter your statistics in My Fitness Pal. While a 2 pound a week goal is possible for you, that doesn't mean you have to choose the most aggressive plan. If you need medical weight loss fast....talk with your doctor.

Choose something like 1.5 pounds a week. 1.5 pound a week goal is going to be more comfortable than 2 pounds a week. Eventually that goal will be lowered to 1 pound a week, then 1/2 pound a week (as you become smaller you requires fewer calories).

B.) Low carb is popular right now. The fatigue you are feeling is likely due "low carb flu".....add more sodium to your diet. This is the thing impresses some people with starting low carb....the water weight loss. The sodium does counteract that, but you feel better.

If you have a medical reason to eat low(er) carb, then do so. If you enjoy eating low(er) carb, then do so. BUT for weight loss, calories are king. Find a way to eat fewer calories. Do that consistently and you will lose weight.

Many people shift the focus "positive:" meet protein goals and meet fat goals. This will naturally lower carbs a bit for many. Just demonising carbs isn't educational or helpful.

Finding satiating foods is a learning experience. Protein, fiber and fat are filling components but it's a little different combination for everyone. Give yourself time to learn what's right for you.

This is a great thread for new comers:
https://community.myfitnesspal.com/en/discussion/10300331/most-helpful-posts-getting-started-must-reads#latest

Maybe you can have a conversation with your doctor. When I first decided to lose weight my doctor also suggested 1200, but asked me if I wanted a referral to a dietitian. I said no, went home, found 1200 too low, ate 1600. Next time I saw him I told him I couldn't do 1200. He said I was doing fine and my weight loss was where he wanted it to be. His initial recommendation was based on the fact that many people tend to be sloppy counters (eyeballing, not counting certain things...etc), so the initial lower number was to account for undercounting.

If you don't need to lose weight urgently and quickly, you can probably talk to your doctor and see if they gave you a lower budget than he expects you to eat.

ETA:
I'm someone who doesn't feel full without carbs. I need my bread and my rice and my beans. I don't think I'll survive without potatoes. I lost 140 pounds eating these things daily, plus fruits (sugar! the horror!). Don't make it harder on yourself than it needs to be. If eating low carb leaves you hungry, then maybe experiment with increasing your carbs and see if that solves the problem.

Another note, and it's strictly personal to me. I really REALLY love nuts, but they don't work for me as a snack. The amount is so tiny, they're gone so quickly, and they don't fill me up.

because MFP uses a NEAT calculation to provide recommendations - this doesn't include purposeful activity; a TDEE calculation would - when you compare the two (logging purposeful activity - they should come out approximately even)