Use application/octet-stream instead of image/jpg:
If [the Content-Disposition] header is used in a response with the application/octet-stream content-type, the implied suggestion is that the user agent should not display the response, but directly enter a `save response as...' dialog.
— RFC 2616 – 19.5.1 Content-Disposition
EDIT
function forceDownloadQR($url, $width = 150, $height = 150) {
$url = urlencode($url);
$image = 'http://chart.apis.google.com/chart?chs='.$width.'x'.$height.'&cht=qr&chl='.$url;
$file = file_get_contents($image);
header("Content-type: application/octet-stream");
header("Content-Disposition: attachment; filename=qrcode.png");
header("Cache-Control: public");
header("Content-length: " . strlen($file)); // tells file size
header("Pragma: no-cache");
echo $file;
die;
}
forceDownloadQR('http://google.com');
if you want to download the file onto your webserver(and save it), just use copy()
copy($url, 'myfile.png');