Some hints how I would solve this:

1. Your date format yyyy-mm-dd hh:mm:ss is already suitable for lexographical sorting, no need to change the format.
2. The date is the last 19 characters of each line, so it can be extracted easily using either a regex or substr.
3. If you read line by line, don't forget to chomp;
4. The Schwartzian Transform is one way to approach this. Read here: Understanding the Schwartzian transform.