First of, note that what you try to do might be illegal since a number of sites prohibit the use of scripts to interact with them. You'll have to check the end user agreement to make sure.

Technically, a number of things went wrong, see the code below for something that seems to work:

my $URL = "http://www.arabidopsis.org/cgi-bin/Blast/TAIRblast.pl";
#BLASTX:NT query, AA db  ->blastx 
#AGI Proteins (Protein)     ->ATH1_pep
#query sequence             ->QueryText
my $response = $browser->post( $URL,
    [ 'Algorithm' => 'blastx', 'BlastTargetSet' => 'ATH1_pep',
      'QueryText' => $sequence,
      'ReplyTo' => 'monk@perlmonks.org'
    ]
);
[download]

Hope this helps, -gjb-