You're right, with this method you copy the whole document.
But you could use the CopyItemToDocument method of the notesItem - class.
Example:
Dim dbNew As New NotesDatabase("" , "MyDB.nsf") 'Target DB
Set docNew = New NotesDocument( dbNew )
'.......
Set itemSender = doc.GetFirstItem( "From" )
Call itemSender.CopyItemToDocument( docNew, "MyItem_Sender" )
Give it a try :-)
Matthias