ANSWER:

A breastfeeding woman can skip fasting without the recommendation of a doctor whether Muslim or kafir if there is hardship or difficulty on her. She must make up for such missed days once she is able. 

QUESTION: If a woman is recommended by kaafir doctor to not fast because she is breastfeeding, is she obliged to feed the baby artificial formula(liquid/powder) milk made for infants/toddles and fast? or can she listen to the recommendation of the kaafir doctor and not fast?