As jellisii2 mentions you do need to include the hidden field 'translationNo'. This worked for me:

my $response = $browser->post( $url,
    { 
        'Sequence' => '42 Escherichia coli (strain K12)',
        'seq_type' => 'DNA',
        'genome' => '42 Escherichia coli (strain K12)',
        'hairpin' => 'checked',
        'quickChange' => 'checked',
        'translationNo' => 1,
    }
);
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