I really doubt that CURLOPT_HEADER has the value you want, in your second example. If you had used strict and/or warnings, Perl would have told you so:

use strict;
require WWW::Curl::Easy;
import WWW::Curl::Easy;
my $curl = WWW::Curl::Easy->new;

$curl->setopt(CURLOPT_HEADER,0); # boom
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You will either need to fully qualify the names of the constants, or import them before your code gets compiled:

use strict;
require WWW::Curl::Easy;
import WWW::Curl::Easy;
my $curl = WWW::Curl::Easy->new;

$curl->setopt(WWW::Curl::Easy::CURLOPT_HEADER,0); # or wherever CURLOP
+T_HEADER gets declared
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