using the example code you provided (modified a little adding a couple semi-colons where needed
and some text to print
it's not displaying the content header in the browser for me on a Mac using Safari or IE

#!/usr/bin/perl
use CGI;
use CGI::Carp qw(fatalsToBrowser set_message);
$CGI::HEADERS_ONCE = 1;

BEGIN {
  sub carp_error {
    my $message = shift;
      error( $message );
  }
  CGI::Carp::set_message( \&carp_error );
}

my $q = new CGI;

# time passes

print    $q->header( 'text/html' );

print "test";
exit;

sub error{
  # die nicely
  exit;
}
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