LWP::Simple does indeed do redirects. (Not javascript redirects though!)
use LWP::Debug qw(+conns);
# This will tell you what's going on.
One bug that has come up in LWP::Simple is on some machines, it just mysteriously fails. Try prepending a space to the url. get " http://yahoo.com;"
Stops it from using _trivial_get internally which is the source of the bug.