When breastfeeding my two I ate freely of low carb foods - no restriction on the amount, but when badgered to eat high carb low fat foods I got a perpetually hungry child, all day and all night, wailing every two hours frantic to be fed and I had to give up due to the damage done to me.
Fasting is not a good idea, nor is any restriction other than high carb foods - but be prepared for strong active inquisitive babies who grow up tall and energetic, and far too clever.