You can use Desktop Task Timer to keep a separate log of your tasks for each day. This allows you to look at historical records and export a range of dates (say, if you are making a weekly invoice).
(Note: you can disable daily timesheets if you'd like the simpler option of just keeping a single list of tasks that you continually update. See the preferences page for more details.)
The current timesheet date is displayed on a large button at the top of the timer window. It will automatically update to the current date if you re-open the window. If you click this button, a calendar control will slide out. Click any date on this calendar to view that day's tasks. If you don't have any tasks for that date, it will display a few blank task rows.
Note that you can select a range of dates for display. Simply click and drag your mouse over several days and the timesheet view will display all of the tasks, in date order, from the days you've selected.
If you are trying to select days across multiple months, it may be easier to use the "shift-click" method to select those dates. To do this, first click on your desired start date. Then navigate in the calendar to your desired end date. Hold down shift and click on the end date, and the calendar will select that range of dates.
When you select a range of dates, the task list will not be editable and the start/stop button will change to 'Export' (see image below). Take a look at the export page for more details.