I have a now 6 1/2 year old who was, and to a certain extent still is, the exact same way. He drinks about a half gallon of milk (skim milk) a day by himself. He refuses to drink any thing else, except water. He REFUSES to eat any kind of meat whatsoever - even if it is hot dogs, bologna, chicken nuggets, etc. He also refuses to eat other "kid loved" foods like cheese, crackers, pretzels, most types of cookies or cakes, pudding, yogurt, pizza, fruit snacks, etc., etc. It's terribly frustrating because my other three kids will eat almost everything. As a mom I have always wondered if he getting enough nutrition, etc. because he refuses to eat so many foods, but my pediatrician reasures me it's okay - and we give him a kids vitamin, but it is the quick dissolve on your tongue type because he won't chew the traditional or gummy ones. For example, the only veggie he will eat is peas and the only fruit he will eat is bananas. But, he will eat almost any kind of pasta or bread. His favorites are spaghetti, chicken flavor ramen noodles, mac-n-cheese, garlic bread.
Here's something else to think about though which is true for my son. Does your daughter have any type of a speech delay? Did she babble much as a baby or not? Did you think that she was a quiet baby who didn't make much noise or fuss? For some children with speech delays those are the first signs that they have a speech delay and they tend to have very picky eating habits - it goes into the whole oral/mouth thing that has too long of an explanation to ramble on about in a posting like this.
Talk to your pediatrician. Good luck!