Much like Juerd said, Learning Perl is good but will get stale fast for someone with a programming background. Don't get me wrong, I like the book and all, but working through all of it seems like it's burning otherwise useful time.

Teaching perldoc is good, I'd also recommend reading perlman:perltrap (at least the first part, I'm sure some parts of the C traps carry from Java well), which I found useful as a CS student transitioning from C/C++/TCL to Perl. Heck, my first question here was answered in perltrap.

If you've got some money, I'd actually recommend picking up the Perl CD Bookshelf 2.0 from O'reilly - it comes with Perl in a Nutshell in deadtree copy, and five books on CD that are handy to search through and whatnot. The first Perl CD Bookshelf had six books, and I don't recall what was eliminated, but CD Bookshelf 2.0 has Programming Perl, Perl in a Nutshell, and the Perl Cookbook, which is excellent to get some understanding from.

~Brian