Nope, not too early to teach them responsibility.
My two elder children, aged 6 adn 4 respectively, are already learning about duties. After breakfast, one of them has to get their vitamins and Yakult and bring them to the table. When they eat biscuits or anything with a wrapper, they have to put the wrapper into the trash. Even my youngest does this now. When they take off their clothes, they have to put them in their hamper. When they come from school, they put their bags and shoes in their proper place. After playing, they put away their toys and books.
I have seen kids and even adults who throw litter on the floor or out the car window. When I see that, I literally want to shove their trash down their mouth. For me, people who are not able to dispose of their trash properly have major discipline and responsibility issues in life.
I have to emphasize that the acts towards teaching life skills to children should turn out to be enjoyable and rewarding for the children. They have to view it as a good thing for them.