As I said in my comment above, you can sub-class the QMdiArea, override its paintEvent() function and draw your logo image yourself (in the bottom right corner). Here is the sample code that implements the mentioned idea:
class MdiArea : public QMdiArea
{
public:
    MdiArea(QWidget *parent = 0)
        :
            QMdiArea(parent),
            m_pixmap("logo.jpg")
    {}
protected:
    void paintEvent(QPaintEvent *event)
    {
        QMdiArea::paintEvent(event);
        QPainter painter(viewport());
        // Calculate the logo position - the bottom right corner of the mdi area.
        int x = width() - m_pixmap.width();
        int y = height() - m_pixmap.height();
        painter.drawPixmap(x, y, m_pixmap);
    }
private:
    // Store the logo image.
    QPixmap m_pixmap;
};
And finally use the custom mdi area in the main window:
int main(int argc, char *argv[])
{
    QApplication app(argc, argv);
    QMainWindow mainWindow;
    QMdiArea *mdiArea = new MdiArea(&mainWindow);
    mainWindow.setCentralWidget(mdiArea);
    mainWindow.show();
    return app.exec();
}