That would mean that if and when she lays a egg it might be fertile---It does not take a rooster/male for the female to lay eggs---only to make those eggs fertile.
It definitely sounds like a breeding pair of pigeons. Just to make you aware same sex pairing do sometimes happen (it is fairly rare I must admit).
my hen pigeon just had her first egg yesterday and she lying on it so is the cock when will she have the second egg