Not sure if your DD is abit young but I have seen this work with 2yr olds.
You can get these mini punching bags or you can use a pillow and everytime she hits take her to the bag or pillow and tell her "we punch the bag/pillow not Mummy." I know it sounds abit weird but hey if it works.. Keep doing it and hopefully she will get it. I also think what you are doing with the putting her down etc is a good strategy. Sometimes children feel angry and frustrated and I think it's good if you can show them how to deal with their emotions early on.
HTH