Take a deep breath and let go of the worrying. Most of the dairy needs in your daughter's life can be filled with dietary items like yogurt and cheese. Also, it is normal for an 11 month old to let the fluid just flow down their chins and chests. For some reason, it seems to give them profound pleasure to do so (I'm basing that on my three children and my nephew). They do outgrow this a little and will drink when they are thirsty. My 11 month old prefers the straw to anything else. When he is thirsty, he will chug down the fluid through the straw. When he is only a little thirsty, he drinks a little and then lets it run down his chin and chest and laughs.
They do outgrow this stage. And she will drink when she is thirsty.
Anyhow, hope this helps. Good luck.