|Perl: the Markov chain saw|
You write that the code you post is your first attempt at a Perl class. As a learning exercise, I think it's valuable to experiment with rolling (or stealing) your own. Perl has a minimal, to me elegant way to get object behavior.
If you'll be playing around a bit, you might like rewriting you class a few different ways. For my simple-minded application, Audio::Nama, I found Object::Tiny's accessors and class creation to be a good starting point. I filled out Alias++'s basic code with simple set() and dump() methods, spent a few days hacking together some YAML-based serialization routines and was on my way. I may change over to Mouse or Moose at some future time.
I found that a good environment to learn the types of compile and runtime errors I would get, how subclassing works, etc.
Regarding your code, first, redefining a subroutine is no big deal: if it's convenient to do so, do it and suppress the warning: no warnings 'redefine'. It's your first class, after all.
Also you may like a more legible format for your default initializations:
All with a grain of salt and some monastery-brewed beer. When it comes to coding style, I am a youngster here.