Drag your object to the Symbols Panel.
This is exactly what symbols are designed to do -- one object with many instances.
To create a duplicate, you can then simply drag from the Symbols Panel to the artboard or use any of the various Symbol Tools in the tool bar.
To edit the symbol, simply double-click it in the Symbol Panel or on the artboard. Right-click/Control-click will also allow editing of symbols. As will highlighting the Symbol in the Symbols Panel and choosing Edit from the Symbol Panel menu. Any edits to the symbol will be reflected in all instances of the symbol.
Utilizing Symbols will also reduce file sizes and speed redrawing, saving, opening, and exporting because with Symbols there is only 1 object, then merely references to that original object. This is much more efficient than storing many copies of the same objects.