Use the following script, which takes advantage of the "I'm feeling lucky" feature of Google:

#!/usr/bin/perl
use strict;
use warnings;
use LWP::UserAgent;

my $search = "bla"; #Your search term

my $ua = new LWP::UserAgent; #Construct the request object
$ua->agent( "Mozilla/5.0 (X11; Linux i686; rv:2.0.0) Gecko/20100101" )
+; #Google checks UAs, so set this to something common
$ua->timeout( 10 ); #Give up after 10 seconds of waiting
$ua->max_redirect( 0 ); #We only want the URL that google sends, so st
+op after we submit
$ua->env_proxy; #Load proxy info from the environment, if any is set

my $response = $ua->get(
    "http://www.google.com/search?hl=nl&btnI=Ik doe een gok&pws=0&luck
+y=1&q=".$search #The URL to request
) or die( $! );


my $firstUrl = $response->header( "Location" ); #This contains the lin
+k of the result page
print $firstUrl;
[download]

Update: I added some comments to the code to make reading a little easier