What happens when you only move your queen

She would need a forwarding address to ensure she receives her mail . . .
As for chess, you would most likely lose the game. With every move your opponent is developing more of his pieces, probably attacking your Queen. As you move her to keep her safe, more of your opponents forces attack her. At some point she is lost. Your opponent has your Queen, has his forces deployed and you haven't developed anything. It's not looking too good for you . . .
Oof