Peter's suggestion for a new national anthem is a remix of the Hamster Dance song which, itself, is a remix of "Whistle Stop," the main title song from Disney's 'Robin Hood.'
Meg is told she is being traded to American Dad. Her other option is The Orville. Both American Dad and The Orville are created by Seth MacFarlane. Note: The Orville however is not an animated show so it would be unlikely that she could go there.