You're confusing two kinds of scripts, one that generates HTML and one that generates an image suitable for use as the src of an img tag.

Here is a simple CGI script that simply generates a page using an image tag:

#!/usr/bin/perl

use strict;
use warnings;
use CGI qw(:all);

my $q = CGI->new;

print $q->header();
print $q->start_html();
print $q->img({src => 'image.gif'});
print $q->end_html();
[download]

And here is the code you want that actually emits the conttents of an image file to be used as the image src:

#!/usr/bin/perl

use strict;
use warnings;
use CGI qw(:all);

my $q = CGI->new;

print $q->header(-type => 'image/gif');
open(my $F, '<', '1.gif') || die "can not open\n";
local $\ = undef;
print <$F>;
close($F);
[download]

Save the 2nd script as img.pl and you can modify the first script to use your second script:

#!/usr/bin/perl

use strict;
use warnings;
use CGI qw(:all);

my $q = CGI->new;

print $q->header();
print $q->start_html();
print $q->img({src => 'img.pl'});
print $q->end_html();
[download]

Notes:

• You don't need two inclusions of CGI, just one with the flag :all to get all the routines
• The image MIME type does not include a character set. It's binary data, there's no concept of character set
• The die in img.pl will never be seen unless you look at web server error logs - the browser expects binary GIF image data and won't show your error message indicating that 1.gif can't be read
• You don't need a script to use img.pl; a static HTML page with an img tag where the src attribute is img.pl is all you need. I just showed you that to show the two types of scripts you are confusing
• You may not be able to use img.pl as your file name; you might have to use img.cgi, depending on how your web server is configureed
• Your Perl may not be in /usr/bin; configure as appropriate for your system
• These scripts assume that img.pl and 1.gif are all in the same directory. This is not necessary; you can use subdirectories.
• Be sure to read the instructions for CGI.
• You may also want to check out Beginner's Guide to CGI Scripting with Perl