You can create a QPainterPath, add the rounded rect to it, and then fill and stroke it:
QPainter p(this);
p.setRenderHint(QPainter::Antialiasing);
QPainterPath path;
path.addRoundedRect(QRectF(10, 10, 100, 50), 10, 10);
QPen pen(Qt::black, 10);
p.setPen(pen);
p.fillPath(path, Qt::red);
p.drawPath(path);
Note that even with antialiasing, 1 px border will probably never really look good, especially on a low DPI desktop monitor, on a high DPI mobile device it will be almost invisible.
If you create the rectangle as QRectF(9.5, 9.5, 100, 50) it will look better with 1 px antialiased border, because it will “snap” on the right pixel:
