Could I breastfeed if I am taking antithyroid medicine for graves' disease?

Maybe. Many pediatricians strongly discourage breastfeeding while taking ptu (propylthiouracil) or methimazole. These meds can affect the baby by lowering his thyroid hormone levels right at the time he needs them for growth and brain development. Others will monitor the baby for any signs of slow growth or get blood tests to check thyroid levels. Close supervision is essential.
Thyroid meds. This depends on what meds and the status of the thyroid. This is question that should be discussed with your primary physician and endocrinologist. The answer can dange from very simple to extremely complex.