It comes after she earlier joined the chorus of voices condemning the senator's speech and remarks on Muslim immigration, saying it was "straight from Goebbels' handbook from Nazi Germany".
Senator Anning said this response proved Senator Hanson had "turned her back on...the people who elected her".
On Wednesday, Ms Hanson introduced a bill into parliament for a plebiscite on how many people come to Australia, arguing it was different to Senator Aning's remarks because it focused on immigration numbers, not who enters Australia.
Speaking on Sky news, the senator has defended the bill.
