I installed Imager::QRCode and PAR::Packer using cpan then used pp test.pl -o test.exe -c -x to generate a 7.8MB test.exe. I got the same results that you did. I then reworked your code to give better diagnostics and to be a little more modern (using lexical file handles):

use strict;
use warnings;
use diagnostics;

use Imager;
use Imager::QRCode;
use Imager::File::JPEG;

my $qrcode = Imager::QRCode->new (
    size          => 2,
    margin        => 2,
    version       => 1,
    level         => 'M',
    casesensitive => 1,
    lightcolor    => Imager::Color->new(255, 255, 255),
    darkcolor     => Imager::Color->new(0, 0, 0),
);                        

my $img = $qrcode->plot('PDJ Test 1');

my @type = ('jpeg', 'png', 'gif', 'tiff', 'bmp', 'pnm', 'raw', 'sgi', 
+'tga');

for (@type) {
    my $fileName = "image.$_";
    open my $image, '>', $fileName or die $!;
    binmode $image or die $!;
    
    my $imageOut = $img->write(fh => $image, type => $_) or die "Creat
+ing $fileName: $!";
    print $image $imageOut;
}
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When packed and the executable is run I get errors like:

Uncaught exception from user code:
        Creating image.png: No such file or directory at script/delme.
+pl line 28.
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As you can see from the sample code above explicitly including the appropriate image file modules fixes the problem (.jpg was a problematic format on my system). You could of course use -M Imager::File::JPEG ... on the pp command line to achieve the same result.