It is not currently possible to copy a timesheet from one week to another. The only way to do this without starting from scratch is to edit each individual time entry and modify the date to the correct week. This will keep all other details about the time entry and will simply update the date. If you'd like, I can add the ability to copy time reports as a feature request on your behalf if you'd like.
If you have any other questions or concerns, please let us know.