I have found the answer!
it is about the drawContents method of QTextDocument.
There is a second parameter that you need to add in order to see the background image in your document.
It's the a QRectF object that represend the size of the rect that the background image will be clipped into.
void QTextDocument::drawContents(QPainter *p, const QRectF &rect = QRectF())
Draws the content of the document with painter p, clipped to rect. If rect is a null rectangle (default) then the document is painted unclipped.
So what I did is:
easuresDoc.drawContents(&painter, pdfPrinter.paperRect()); // We print TextDocument of the Measures into the document
pdfPrinter.newPage(); // We inject the current page and continue printing on new page
averagesDoc.drawContents(&painter, pdfPrinter.paperRect()); // We print the TextDocument of the Averages into the document
pdfPrinter.newPage(); // We inject the current page and continue printing on new page
inOutDoc.drawContents(&painter, pdfPrinter.paperRect()); // We print the TextDocument of the Inputs/Outputs into the document
pdfPrinter.paperRect is the rectangle of the page without the margin.
Also if you want the background image to be printed scaled with no repeat than you need to put the printer into QPrinter::PrinterResolution
QPrinter pdfPrinter(QPrinter::PrinterResolution);