Thank you for reaching out to us, and mazal tov on the birth of your baby!
Generally speaking, if both mother and baby are healthy at this stage, and breastfeeding is going smoothly, then the basic halacha is to try to complete the fast as long as they remain healthy over the course of the day.
It is important to clarify the health issues in advance, by speaking with your and your baby’s physicians about whether there is any special concern in your case, or under what circumstances they would advise stopping a fast. Try to convey to the doctors (even if they aren’t religious, or aren’t Jewish) a sense of the seriousness of this fast.
Be sure to drink extra in the days leading up to the fast in order to prevent dehydration. Arrange to spend the fast in a cool place, resting and breastfeeding. Halachically, your fast takes precedence over going to synagogue – and over your husband’s going to synagogue, if you need his help at home.
To reduce potential stress towards the end of the day, it can help to have one or two bottles of expressed milk available. This should be used after nursing if the baby is fussy, not instead of a nursing session.
Arrange to spend the day or two after the fast resting and relaxing with your baby, nursing frequently to help ensure that you recover and your milk supply remains steady.
If you have previously experienced problems with fasting and breastfeeding, or if you have additional concerns, please discuss with a halachic authority the possibility of drinking and eating in shiurim (less than the measure subject to the Torah penalty of karet). Please see our article on Breastfeeding & Fasting for a more detailed discussion of these halachot, as well as some practical tips.
Please let us know if we can be of further assistance.
Ketivah v’chatimah tovah!