Even at a very early age, children like to emulate activities of both parents and their older siblings. We've all seen a two year-old try to sweep the floor or help mix cupcake batter. What better time to start nurturing this almost innate sense of family.
It is never too early to help your child develop a real sense of family responsibility. We all know kids in their teens, and even twenties, that feel a sense of 'entitlement' about everything. They act like everyone owes them and that they don't need to do their part in the family. If children are taught, as young children, that they are an integral part of the family and, as such, they have an important part in the family, then this will help them to develop a greater family bond.
By letting young children help to do things, such as dusting, sweeping with a little broom, wiping out sinks and baking cooking, it will give them a feeling of accomplishment and pride in doing a good job. Always be sure to praise your child, letting them know what a wonderful job they have done.
As far as giving an allowance to a child, it is probably best to start this practice after the child is of school-age. It is more important to really stress the issue of family responsibility prior to that age. If, and when, you start giving an allowance, it is essential that your child realize that the allowance is not being given for a specific job. Rather, you have chosen to pay an allowance for a combination of things, such as good behavior, good schoolwork, doing chores and family cooperation. Explain that you want them to learn about handling their own money and the choices it entails. This would also be an opportune time to reinforce the value of family and helping each other out whenever possible.
As you encourage your young child in learning about family responsibility with little jobs around the house, remember that the values you teach will travel with your child throughout his life.