Your systax does NOT match that which is documented for 1.03 & 2.00:
use Readonly;
# Read-only scalar
Readonly::Scalar $sca => $initial_value;
Readonly::Scalar my $sca => $initial_value;
Version 1.03 is very old: From CPAN: "This documentation describes version 1.03 of Readonly.pm, April 20, 2004). " The more recent version is 2.00 (with a different maintainer) and a copyright date of "2013-2014." (And that doesn't begin to address the archaic versions of Perl you mention -- 5.14 and, even more so, 5.02... which, if correct makes the "aside" below relevant).)
Aside; unknown relevance but perhaps of interest from the 2.00 doc:
Please note that most users of Readonly no longer need to install the companion module Readonly::XS which is recommended but not required for perl 5.6.x and under. Please do not force it as a requirement in new code and do not use the package variable $Readonly::XSokay in code/tests. For more, see "Internals" in the section on Readonly's new internals.
Updated markup and s/"The version you're using.../"Version 1.03...."/p>