A really good form of exercise for learning Perl is to attempt to answer Seekers of Perl Wisdom questions. You don't need to post your answer, although some times you may wish to raise a question of your own when your solution doesn't behave as expected.

The nice thing about SoPW questions is that many of them are in the context of real problems and that you very often get a wide range of solutions with discussion of their merits. The other thing is that there is a huge number of them - sufficient that with a little searching you are sure to find questions that are of interest to you and match your current experience level.