You might mention that these drugs are frequently used for young
babies, and the evidence is that there is absolutely no need for the
mother to stop breastfeeding.  There is no problem getting a tiny bit
of steroid over such a short period of time.  Furthermore, the
pediatrician is overestimating the half life of prednisone.  You could
mention that perhaps he is so busy that he has not kept up on the
lactation literature.

You might also mention that breastfeeding protects against the baby's
developing asthma and that she should be reluctant to introduce a drug
(infant formula) which has a side effect of increasing the risk of
asthma as well as diabetes...

Jack Newman, MD, FRCPC