I would wait to introduce your daughter to your girlfriend until you are pretty sure this is going to be a long term thing (ie you are knowing you are headed toward getting married even if not in the wedding planning stage). And even after your introduce them, you need to give your daughter a chance to get to know your girlfriend before she starts sleeping over when your daughter is there. This is also something you are going to want to let her mom know. Until you are ready to let her mom know (which you might be now), you need to wait. You don't want her mom to find out from your daughter that your girlfriend is staying over. That could just start a huge amount of trouble. (you would know if this would cause a problem).

My advice would be to have them meet at somewhere other than the apartment. A short visit to introduce them and then increase the time as it goes on. Good luck.