No. Eating "the least amount of food" is not better. Firstly because turkey is more nutrient dense than vegetables. You would have to eat a MOUNTAIN of vegetables before getting the amount of nutrients in a turkey dinner, for example. It's like weighing feathers and lead - a pound of lead will take up less space than a pound of feathers, but you are still going to be having "a pound" of something. So you can't think to yourself "I ate a turkey rather than a mountain of broccoli, therefore I ate less food" because that simply isn't the case at all. It's nutrients that matter, not the bulk of food you ate.
Secondly and more important, the Low Everything Diet is meant to be a safe and healthy pre-pregnancy diet. It is NOT a starvation diet. The goal of this diet is not to eat as small an amount as you can stand. You are eating a normal diet, to enable yourself to get and stay pregnant with a healthy baby, but it's just the lower end of normal. That will help you be more likely to have a girl.