To bridget - really this is a completely healthy diet. It is not no carb and no fat overall, but it is for the first two weeks. You are eating low fat meats which includes some fish which you shouldn't have while pregnant. You are eating a lot of green veggies which is awesome, but not a lot of other veggies and no fruit. Again - this is the first two weeks.
While I completely support this diet, I think you are not getting all you need to give a baby and yourself. I would say, wait until you are not even breastfeeding to start this. Fat is good for babies brains while they are developing inside and outside of you!
Btw - I was 130 with my first baby and gained 50 pounds with him. I ate bacon and spaghettios a lot. Yuck. I was 194 pounds when I got pregnant with my second baby five years later. I weighed 212 when I gave birth. I only gained 18 pounds with her, because I actually started eating healthy foods and I was very overweight. So it is possible to lose weight while pregnant. I didn't plan it, but it happened. I ate chicken, beef, tons of fruits and veggies and plenty of dairy, too.
Good luck to you and your future blessing!