Doing something that is already been done is not an empty exercise. It is real life learning. Re-implementing a CPAN module is an opportunity to understand how someone can get to a solution. And if you don't "cheat" (Look at source of the original module) you can test your solution against a (hopefully) known working solution
in reply to Learning by Doing
This will allow you to work to a solution, which in my mind is more important then being original at this time. Everyone wants to be unique, but what most employers are looking for are people who can finish a task.
Other options mentioned, such as the Apprenticeship site and finding repetitive task you do at home are very good. But you need to show follow through and finish what you start.
Who needs a spiffy sig.