First, yes, you will need to reinstall Outlook.
Now, when you log onto Outlook for the first time, it will create your .ost file, this is your data file. So you do not need to export that.
As to your calendar, tasks, .pst, and contacts, yes, you can and will need to export those, unless they are kept on the exchange server. Are you logging onto the same network? If so, other than your personal folder, .pst, then that is all you will need to export and take with you.