I'm not familiar with "Converter.pm". You probably need to pass the hash by reference. It could even be an anonymous hash, in which case, your syntax is very close. You just need the anonymous hash constructor:

my $status = $document->convert(
    {    'MIME-Type'  => 'application/ms-word',
         'Input'      => '[In file]',
         'Output'     => '[Out file]
    } );
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