JIRA has built-in time tracking, or you could use Tempo if the built-in feature is not sufficient.
Reporting
For the report, you can create a custom template for the Better Excel Plugin. This would just iterate through the worklogs of each issue, then calculate the earliest and latest dates, then export those with the field values to a spreadsheet. See the customization guide.
There is a default template that processes worklogs to create various reports. You could use that as starting point.
