If you’re able to, the easiest thing to do is use a QToolButton instead:
QToolButton* button = new QToolButton(this);
button->setToolButtonStyle(Qt::ToolButtonTextUnderIcon);
button->setIcon(myIcon);
button->setText("Sample text");
If that’s not an option you could consider creating your own button widget, possibly derived from QPushButton or QAbstractButton. In this case you’ll probably (I haven’t tried it myself) want to focus most of your efforts on reimplementing paintEvent().
[Edit: read the comments for alternatives which are probably way simpler than this]