I am so sorry. I think you are very brave and kudos to you for doing the right thing by your child, the most important person involved!
I have a DD who turns nine next month. I have discussed her father's addiction with her and her sister very open and honestly, in an age appropriate way, for a long time. I also take her to see a counselor who specializes in helping families with addiction issues. She loves her counselor and it has been a God send!
Good luck to you. Hold your head high and be comforted that you just saved your DD's life and sanity.