PNG is not designed to represent real world objects in any other sense, than what they look like. It is not designed to perform measurements of such objects.
PNG is a bitmap graphics format. A bitmap is a matrix of X by Y pixels. A pixel is not a physical unit.
There is one anchor into the physical world: Pixels can be correlated with the DPI value. Eg at 300 DPI, 600 pixels correspond to two inches. Eg at 10 DPI, 600 pixels correspond to 60 inches.
So you have to place the bitmap into QCAD, then set its width to the width in pixels of the bitmap divided by the DPI value of the bitmap. Voilà, you can use all the QCAD measuring tools on it.
Still, I highly doubt, that your PNG file was created with this use in mind…