The first thing learning C would do for you is give you a much better appreciation of Perl. You'll quickly learn all the tedious tasks that Perl hides from the programmer, and what really has to hapen when you do a  $name = $first . $last. My most common thought when I first started to learn Perl was, "Wait! You can't do it like that!" It was a struggle for me give in to the simplicity you'll find in Perl.

And as others have mentioned, you'll learn a lot about memory allocation and management. With Perl, this is one of the things that just happens. With C, you're responsible. Take a look at Why Not Translate Perl to C? for a very brief example. Read the whole thing. It will also give you some insight into the magic that Perl performs.

Hope this helps..
Rich

P.S - Take a look at Practical C Programming. My youngest brother (15) wants to learn how to program and I got him this book. He's going to learn C first to appreciate how easy other languages are :)