Hi Life is Good,

I don't know the answer in relation to breastfeeding specifically (although I am aware protein is important while BF), but it might be better for you to consider low GI carbs instead of no/few carbs. Carbs aren't bad in and of themselves. Simple carbs (sugar, potato, white flour) are the ones you want to avoid. Complex carbs (grainy bread, vegetables, legumes) are important in providing energy.
Hope this helps!