<p>Why can I not see an <strong>option</strong> for copying database objects when I <code>right click &gt; tasks</code> on my database? </p>

MS Sql Server Express doesn't come with SSIS which is what you will need to import/export objects out of your database.
You can also manually script this process. One way is to use BCP (
http://msdn.microsoft.com/en-us/library/ms162802.aspx
)