To go SUMMER SLEDGE RIDING down the hill from Schliersbergalm would probably be big fun for your daughter.
Visit the website (German language only):
See what summer sledge riding (= Sommerodeln) is like:
http://www.almtv.de/CMS/index.php?option=com_content&task=view&id=24&Itemid=53
http://www.schliersbergalm.de
You can take the cable car to go up to Schliersbergalm if you don't want to walk. The cable car station is about 15 minutes away from the train station.
The lake Schliersee is 5 minutes away from the train station. There you can go on a boat trip or rent your own boat.
HOW TO GO TO SCHLIERSEE:
You take the BOB (= Bayerische Oberland Bahn) from Munich main station to Schliersee. It takes you about 45 min to go there.
A decent restaurant with a big choice of food which is close to the train station in Schliersee is called "Steakalm am Pfeiler". (don't confuse it with Schliersbergalm)
I strongly recommend you to visit Schliersee (and not Tegernsee or Rottach Egern) together with your daughter because there are more things to do for children. Furthermore Schliersee is a smaller town where you can walk all distances.
I grew up in the area. Therefore I know all the places quite well.