Excellent answers so far, I especially liked the recommendations for learning about unit testing.
I wouldn't say that object oriented is more advanced than functional, it's just a different way to do something. The biggest benefit I get from OO is the ability to keep state, as well as being able to include objects within other objects and the ability to pass objects around as other function/method (a method is a function that is called through an object or a class) parameters.
Although there have been great recommendations so far, I like to plug Learning Perl Objects, References and Modules by Randal Schwartz whenever I can (more for the references part, but if you want to advance, mastering references is a very good place to start, as that's what an object is anyway). This book covers a few topics that will get you going forward.