My daughter is almost 3, I started giving her chores to do about 4 months ago...?

Nothing too hard, just putting some dishes away(her little dishes), putting her laundry in the hamper, cleaning her room. But lately she wants to do more of what I do, washing dishes,vacuuming,etc. Should I give her more resopsibilty or is this a case of monkey see/ monkey do? Should she even have chores yet? She is my first child, so I'm still clueless on some things.