@Qjay
This may not help because I do not know quite how you would do this directly from Qt, but when we want to print a PDF under Windows we use the underlying Win32 function ShellExecute() (https://msdn.microsoft.com/en-us/library/windows/desktop/bb762153(v=vs.85).aspx) to go (effectively) ShellExecute("print", native-path-to-file), and let Windows shell sort it out.
This is effectively the same as right-clicking on the file and picking the Print action. So you don't need to know anything about the actual process which does the printing, its arguments etc.