Before the age of 2 you don't need to book a seat. You can book one on every airline I flew with when my son was <2 at least. A child under two needs to be on the lap of a parent during takeoff and landing but can otherwise use a seat. I flew with my son first time when he was about 3 months old, and we had a seat for him because it made it a lot easier.
She booked an adult seat, but was (according to their broken system) 1 years old while doing so. That's different than booking an extra seat for an accompanied infant.
In this case, she did book a seat.