That's not something our login module would implement. There are Joomla plugins out there that can help to email you, or log, authentication events. Those events wouldn't be specific to our login module, but would work for any module. That's the nice thing about Joomla is that there's different bits and pieces for different functionality. Our module is mainly meant for the front-end, user facing, easy to use aspect. Some user plugins are what you sound like you're looking for to add some more administration type features to the authentication process.
I don't have any suggestions as to what to look at, but the Joomla Extension Directory should be able to help you find the right thing for your needs.
I hope that helps explain, but if you have any other questions, just let me know.
Thanks,
Alex