Scripture does not suggest that the child was unclean. It was only the discharge of blood that made the mother ceremonially unclean. The discharge of blood is mentioned three times in this chapter as the reason for uncleanness. This is confirmed by the parallel in Leviticus 15:19–24.
2 Parle aux enfants d'Israël, et dis: Lorsqu'une femme deviendra enceinte, et qu'elle enfantera un fils, elle sera impure pendant sept jours; elle sera impure comme au temps de son indisposition menstruelle.