In the current versions of WWW::Mechanize, the _do_request method (which was considered private anyway) has been superseeded by the request() method. So most likely you will be able to replace that line by

$agent->{res} = $agent->request($agent->{req});
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Note that I did not test this, as I don't have access to WWW::Mechanize in a testable form here.

perl -MHTTP::Daemon -MHTTP::Response -MLWP::Simple -e ' ;    # The  
$d = new HTTP::Daemon and fork and getprint $d->url and exit;#spider
($c = $d->accept())->get_request(); $c->send_response( new   #in the
HTTP::Response(200,$_,$_,qq(Just another Perl hacker\n))); ' #  web
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