I've tried to submit the form using the submit method, but it seems the first form on the page (a website search box) is submitted instead of the login form.

I sort of doubt that can happen

use strict;
use WWW::Mechanize;
use WWW::Mechanize::FormFiller;
use URI::URL;

my $agent = WWW::Mechanize->new( autocheck => 1 );
my $formfiller = WWW::Mechanize::FormFiller->new();
$agent->env_proxy();

  $agent->follow('http://use.perl.org/');
  $agent->get('http://use.perl.org/');
    $agent->form(1) if $agent->forms and scalar @{$agent->forms};
  $agent->form_number(2);
  { local $^W; $agent->current_form->value('query', 'WWW::Mechanize');
+ };
  $agent->submit();
__END__
C:\>perl -MWWW::Mechanize -e"die WWW::Mechanize->VERSION"
1.11_01 at -e line 1.

C:\>perl -MWWW::Mechanize::Shell -e shell
Module File::Modified not found. Automatic reloading disabled.
SetConsoleMode failed, LastError=|6| at C:/Perl/site/lib/Term/ReadKey.
+pm line 268.
>open http://use.perl.org/
Use of uninitialized value in concatenation (.) or string at C:/Perl/s
+ite/lib/WWW/Mechanize.pm line 1743, <IN> line 1.
Can't find any link matching http://use.perl.org/ on this page () at C
+:/Perl/site/lib/WWW/Mechanize/Shell.pm line 1028
Can't call method "code" on an undefined value at C:/Perl/site/lib/WWW
+/Mechanize/Shell.pm line 1034, <IN> line 1.
>get http://use.perl.org/
Retrieving http://use.perl.org/(200)
http://use.perl.org/>
http://use.perl.org/>
http://use.perl.org/>forms
Form [1]
GET http://use.perl.org/search.pl
  query=                         (text)
  <NONAME>= Go                   (submit)
Form [2]
GET http://search.cpan.org/search
  mode=module                    (option)   [*module/Module|dist/Distr
+ibution|author/Author|doc/Documentation]
  query=                         (text)
  <NONAME>=Search                (submit)
Form [3]
POST http://use.perl.org/login.pl
  unickname=                     (text)
  returnto=//use.perl.org/       (hidden readonly)
  op=userlogin                   (hidden readonly)
  upasswd=                       (password)
  login_temp=<UNDEF>             (checkbox) [*<UNDEF>/off|yes/Public T
+erminal]
  userlogin=Log in               (submit)
http://use.perl.org/>form 2
GET http://search.cpan.org/search
  mode=module                    (option)   [*module/Module|dist/Distr
+ibution|author/Author|doc/Documentation]
  query=                         (text)
  <NONAME>=Search                (submit)
http://use.perl.org/>value query WWW::Mechanize
http://use.perl.org/>submit
200
http://search.cpan.org/search?mode=module&query=WWW%3A%3AMechanize>
http://search.cpan.org/search?mode=module&query=WWW%3A%3AMechanize>
http://search.cpan.org/search?mode=module&query=WWW%3A%3AMechanize>scr
+ipt foo.pl
[download]

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