This is untested, probably unsafe and assumes unix. The basic idea is simple, if we aren't on the remote host copy ourself there otherwise do what we were written for.

use strict;
use warnings;

use Sys::Hostname;

chmod 0700, $0;

my $remote_host = 'somewhere';
my $user_name   = 'somebody';
my $password    = 'something';

if ( hostname ne $remote_host ) {
    require Net::SFTP;
    require File::Basename;
    require Net::SSH::Perl;

    my $remote_file = basename $0;
    my $sftp        = Net::SFTP->new(
        $remote_host,
        user     => $user_name,
        password => $password
    );
    $sftp->put( $0, $remote_file );
    my $ssh = Net::SSH::Perl->new($remote_host);
    $ssh->login( $user_name, $password );
    $ssh->cmd($remote_file);
}
else {
    unlink $0;

    # do your stuff here
}
[download]

I've also assumed that you can install all the required modules;-)