Hi Thomas,
QuarkXPress Server’s direct PDF output does not allow you to save in PDF 1.3 format: Erik's post is correct, the best way to achieve this would be to create PostScript and save out to a Distiller watch folder (using a request in the format http://server:port/saveas/postscript/document.qxp?path=c:\distillerfolder&savetopool=false&newname=postscript.ps), assuming distiller can be configured to make the PDF format you’re looking for.
You could alternatively set up the PDF preferences for QuarkXPress Server to always print ‘Postscript for later distilling’ - when selecting this setting in the preferences, you can choose the watch folder for distiller: if this setting is made, then all PDF requests will be saved as Postscript to the Distiller watch folder, rather than using the Quark PDF engine.
Hope this information helps!