If your wife fears on her life or the life of baby by breastfeeding while keeping fast, she can leave the fast of Ramadan and make its qaza later. And if she does not have any fear by breastfeeding, then it is necessary to keep fast, it is not lawful to miss it.
الحامل والمرضع إذا خافتا على انفسهما أو ولدهما أفطرتا و قضيتا و لا كفاره عليهما (عالمگیری).
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband