The first thing you need to understand is the difference between a body and a component.
Sketches can have several different uses, but most often they are used to create the base shape for a body.
Both the sketch and body created from it might live in a component.
To create a independent copy you can copy and then paste new that component.
To make sure everything is created in the component you should follow Fusion 360 R.U.L.E #1: Before doing anything, create a component and make sure it's activated.
For newly created components activation is automatic. Activating a component will ensure that all objects such as sketches, bodies, construction geometry its are created in that component.