As long as your niece is planning to fly with the newborn as a "lap infant" (i.e. without a separate seat for the infant), I would suggest the following:
1) Call LO to review the steps below and confirm this will work.
2) Have the niece book her adult ticket.
3) Once booked, call LO to reserve a bassinet (if she wants one). There is no lap infant on the reservation yet, but perhaps LO can put comments on file about a future lap infant to justify the bassinet. Worth a try.
4) Once the baby is born, call LO to add the infant to the existing adult reservation.