It doesn't appear Laravel has a method for doing this in the manner you mention. However, it would seem you should be able to use the run method to execute the redis auth command just as you would any other method. You would do this after creating the connection.
Redis doesn't authenticate when connecting, it implements a command to handle authentication as documented at http://redis.io/commands/auth
As for storing the password in the config file, it would also likely be a matter of adding a variable to the config and referencing it as you would any other config variable.