Perldoc is not a part of the Perl language. It is a program that is part of the core distribution. You'll likely find a perldoc.bat in your ActivePerl install if you look for it.
So that's why:
perldoc perldoc
works from the command line (because that's how it is intended to be invoked. But fails miserably when you ask Perl to execute 'perldoc' command. It tries valiantly to find a method, defined somewhere in all of the modules that have been included, but finding none, tells you so.
So if you want to write a Perl program to execute perldoc, you could use something like this:
print `perldoc perldoc`
But you're much better off using a bat file, or its equivalent in your version of windows.