When I started with perl, I had a copy of the Llama book (Learning Perl - it was very good back then, including material that isn't in the docs that come with perl, I presume the current edition is just as good) and quickly got a copy of the Camel book (Programming Perl - maybe not so useful these days now that everyone has enough screen space to edit their code in one window while using perldoc -f in another).

But most of my learning wasn't from those books. It was from finding and downloading other peoples' code that did almost what I wanted but not quite. To get exactly what I wanted, I had to read the code, understand how it worked, and fix it. So I read lots of code, gained a good understanding of it, and wrote a little bit. This was done at work, with deadlines, and it's purely by luck that I fell into using perl instead of any other language: I simply found perl stuff that almost worked before I found anything else that almost worked :-)

I don't guarantee that that will work for you, of course, but it's an approach that might be worth trying.