What you have learned so far is basic, elemental Perl. There are many problems that can be solved with what you know so far.
When using Perl for larger more complex applications you will need to learn about references, modules, packages, and the object model of Perl. Object oriented Perl is fully capable and, as usual, there are many ways to do it. Modern Perl has a module called Moose that enhances the object model in many ways.
The best next step is to get a copy of the O'Reilly book, Intermediate Perl, read it carefully, and try everything for yourself!
Here is a tar file containing the 12 files on the Downloads section of www.intermediateperl.com.