One thing you may consider is a Systems Admin job.
in reply to Where would you look for your first job?
As a systems admin, you'll almost certainly encounter an endless stream of opportunities for automation and improving existing systems and processes. And this is one area where Perl really shines - so it would be a very good environment for improving and honing your Perl skills.
Another place to look might be a Network Operations Centre (NOC). This is one place where somebody with Perl skills is almost always welcome.
Hope this helps,