If the browser supports Netscape's "refresh" headers (and what browser doesn't, these days?), you can give it a few seconds in which to render the page before redirecting.

To demonstrate, here's a variation of friedo's code:

#!/usr/bin/perl

use strict;
use warnings;

use CGI;

my $q = CGI->new;
my $delay_seconds = 4;
my $url = 'http://somewhere.com/';
print $q->header( -type => 'text/html', 
                  -refresh => "$delay_seconds; $url",
                );

print "<h1>Here's some HTML.</h1>";
[download]

Tested with Firefox and Apache.