I'm thinking of sweeping the dust into my brothers room whenever I sweep my room
Why do you want to do this?
Yes, he always neglects to dust himself
I'm sorry you get so frustrated. It's rude to sweep dust into someone else's room. If he doesn't clean then that is up to him, you shouldn't let it bother you.
Are you stupid? He needs to fuck off.
Making him clean other peoples dust is unfair. He has his own room, have you told your parents he doesn't do the chores? They have more power and and can punish him for slacking off.