I just discovered that it is possible to add a Search Query as a Favorite by dragging it from the History pane.
The only difficulty is that the actual query does not show up in the entry name in the history panel.

Once search is identified, however, it can be dragged to the Favorites pane and renamed there by right clicking on the entry and choosing rename.

Perhaps an simpler implementation would be to enable dragging an entry from the Search History drop down list to the Favorites pane and using the name as it is listed there?
Of course, adding it by right clicking on a history entry item would be nice too.
