The rash of poison ivy is an allergic response to the oils of the plant (or
other members of the Rhus family). Once the oils are washed off, the rash is
not contagious.
 It seems to spread because the timing of the rash depends upon the
sensitivity of the skin and the amount of oil from the plant.
There would be no risk to the infant. Mom would have to watch out for signs of
secondary infection which may be increased because the baby may rub off the
damaged skin as she nurses.