Like briefinterviews mentioned, it will vary among programs. Generally, I have seen most programs begin accepting applications from October through January. Some Cal State schools take applicaitons til March. I would encourage sending in your application a little early, at least by December. Most students do not hear from the program until March or April.
A LCSW is great! I'm happy you are exploring that option. I'm not sure what your experiences are, but I would take these next months building up your experience. Most MSW programs will have an option you can declare: Child and Family, Mental Health, Nonprofit Management, etc. Make sure you look at the available options. With background experience and a potential focus on the population you want to serve, this will strengthen your personal statement. Oh, and some programs might require the Revised GRE (in which case, you will need to study!)