Ok, just so anyone else trying to do the same thing has an answer, here's what I did:

Qt Code: 
  1. //In the constructor for the Header subclass
  2. m_styleSet = "QHeaderView::down-arrow { image: url(:/images/down_arrow.png); width: 13px; height:9px; subcontrol-position: bottom right;} "
  3.     "QHeaderView::up-arrow { image: url(:/images/up_arrow.png); subcontrol-position: bottom right; } "
  4.     "QHeaderView:: section { color: %1; background-color: %2; }";
  5.  
  6. QString setStyle = m_styleSet.arg(QApplication::palette().windowText().color().name()).arg(QApplication::palette().window().color.name());
  7. this->setStyleSheet(setStyle);
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I installed an event filter:

Qt Code: 
  1. bool CHeaderView::eventFilter(QObject* obj, QEvent* event)
  2. {
  3.    if ((event->type() == QEvent::ApplicationPaletteChange) ||
  4.       (event->type() == QEvent::PaletteChange))
  5.    {
  6.       QString setStyle = m_styleSet.arg(QApplication::palette().windowText().color().name()).arg(QApplication::palette().window().color.name());
  7.       this->setStyleSheet(setStyle);
  8.       return true;
  9.    }
  10.    return QHeaderView::eventFilter(obj,event);
  11. }
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This allows for palette changes & still gives me the arrow that I want (the .pngs)

Vycke