The solution is far more easier than I thought (tested under Qt 3.3.5 on PLD Linux):
Qt Code: 
  1. #include <qapplication.h>
  2. #include <qheader.h>
  3. #include <qlistview.h>
  4. #include <qpushbutton.h>
  5. #include <qvbox.h>
  6.  
  7. class Test : public QVBox
  8. {
  9.    Q_OBJECT
  10.    public:
  11.       Test() : idx( 2 )
  12.       {
  13.          _lv = new QListView( this );
  14.          _lv->addColumn( "A" );
  15.          _lv->addColumn( "B" );
  16.          _lv->addColumn( "C" );
  17.  
  18.          new QListViewItem( _lv, "a1", "b1", "c1" );
  19.          new QListViewItem( _lv, "a2", "b2", "c2" );
  20.          new QListViewItem( _lv, "a3", "b3", "c3" );
  21.  
  22.          QPushButton *pb = new QPushButton( "Switch", this );
  23.          connect( pb, SIGNAL( clicked() ), this, SLOT( switchColumns() ) );
  24.       }
  25.  
  26.    private slots:
  27.       void switchColumns()
  28.       {
  29.          _lv->header()->moveSection( 0, idx );
  30.          _lv->triggerUpdate();
  31.          _lv->header()->update();
  32.  
  33.          idx = 2 - idx;
  34.       }
  35.  
  36.    private:
  37.       QListView *_lv;
  38.       int idx;
  39. };
  40.  
  41. int main( int argc, char **argv )
  42. {
  43.    QApplication app( argc, argv );
  44.  
  45.    Test mw;
  46.  
  47.    app.setMainWidget( &mw );
  48.    mw.show();
  49.  
  50.    return app.exec();
  51. }
  52.  
  53. #include "main.moc"
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