Is there a way that I can simply "copy" or "replicate" what I have on my laptop onto the Servers?

Yup, thats what Perl::Dist::Strawberry does to create strawberryperl

http://www.citrusperl.com/helpweb/createdistribution.htm, http://www.cavapackager.com/appdocs/contents.htm, PPM Make, PAR