Do you have to use Term::ReadLine? If not, see perldoc -q password.

             First, you put the terminal into "no echo" mode,
             then just read the password normally.  You may do
             this with an old-style ioctl() function, POSIX
             terminal control (see POSIX or its documentation the
             Camel Book), or a call to the stty program, with
             varying degrees of portability.

             You can also do this for most systems using the
             Term::ReadKey module from CPAN, which is easier to
             use and in theory more portable.

                 use Term::ReadKey;

                 ReadMode('noecho');
                 $password = ReadLine(0);

Probably easier using Term::ReadKey.