How fast can the average woman lose on 1200 calories a day

I'm new here, I am trying to get to the point where I can actually have surgery. Right now my BMI is much too high. So I am supposed to lose weight. The problem is, the doctor wanted me to go on Optifast to lose weight. I would if I could, but since it has dairy in it, I am not able to go on it. My problem is not just lactose intolerance but I have Food Protein Induced Colitis. So I get very very sick from even a small amount of dairy due to the proteins (casein and whey) that is in dairy.  

So I need another way to lose weight. I have eaten a low cal diet a long time ago and lost weight, on my own, so I know how to do it. But I am wondering...

Would anyone know how fast someone who is 375 lbs and sedentary could lose weight on 1200 calories a day?  Should I be eating less than that? I need to lose weight quickly because I have a hernia and am having trouble with it but they cannot operate on me at this weight. 

Thank you so much if you can give me an idea...

Have you actually tried the Optifast?  I just ask because I"m casein intolerant and whey intolerant and yet was able to tolerate it....

There are other shakes out there that would suit you - egg protein, hemp protein, pea protein all come to mind.  

I had a BMI of 72.6 when I started my process and and right at 70 the day of surgery.  It was never an issue.  Of course, the only comorbidity I had was sleep apnea so everyone is different.  Just know that some surgeons do work with larger patients.  I understand that losing weight would make the surgery less risky, of course.

Fitday.com will estimate how many calories you need to take in to lose X amount of weight within a given amount of time.  I suspect myfitnesspal will too.  I recommend at least a little walking in addition to the calorie restriction, as well, though.  It will make the recovery process easier if you are more mobile.

I'm going to do my best to answer your specific question, based solely on the math.  Let me say at the outset that I would not go under 1200 per day without Doctor approval since you are pre-op. 

A reasonable estimate for the calories you need per day to maintain your current weight is to multiply your body weight by 10.  (In other words, ten calories per pound to maintain.)  At a weight of 375 pounds, you need 3,750 calories a day to maintain.

So, if you are consuming 1200 a day, then you have a deficit of 2550 each day that your body takes from its fat reserves. (i.e. 3750-1200=2550)

To lose a pound of fat, you need a deficit of 3500 calories.  

Therefore, here is roughly what you can expect to lose:

At one week: 2550x7=17850/3500= 5.1 pounds in a week

Over two weeks: 2550x14= 35700/3500= 10.2 pounds over two weeks

One month: approximately 22.58 pounds

Hope this helps!