Looking at the LWP::UserAgent manual page and grepping for redirect gives a couple of options you can give as a parameter for new that may do what you want. Searching for redirect further down gives you a couple of useful handlers you can use. And even further down, we stumble upon:

       $ua->simple_request( $request )
       $ua->simple_request( $request, $content_file )
       $ua->simple_request( $request, $content_cb )
       $ua->simple_request( $request, $content_cb, $read_size_hint )
           This method dispatches a single request and returns the res
+ponse
           received.  Arguments are the same as for request() describe
+d above.

           The difference from request() is that simple_request() will
+ not try
           to handle redirects or authentication responses.  The reque
+st()
           method will in fact invoke this method for each simple requ
+est it
           sends.
[download]

And if that's not enough, there's more that a search for redirect reveals in the manual page. There's also the redirect_ok callback.

Wouldn't you agree that grepping manual pages is much faster than writing a post on Perlmonks and waiting for an answer?