The following code results in a 3x18 pixels dash being drawn instead of a 3x3 dot:

#include <QPainter>
#include <QImage>

int main()
{
    const int w=1000, h=1000;
    QImage img(w, h, QImage::Format_RGBX8888);
    {
        QPainter p(&img);
        p.fillRect(0,0,w,h,Qt::black);
        p.scale(w,h);
        p.setPen(QPen(Qt::red, 3./w, Qt::SolidLine, Qt::RoundCap));
        p.drawPoint(QPointF(0.1,0.1));
    }
    img.save("test.png");
}

Apparently, this is due to the fact that QPaintEngineEx::drawPoints renders points as line segments of length 1/63., without any attempts to adjust the amount of this shift in X direction according to current scale (the one set by QPainter::scale).

So, either QPaintEngineEx::drawPoints should be fixed to take scale into account, or the documentation for QPainter::drawPoints should be updated to mention this peculiarity.