I have a bachelor's degree in music, and I teach piano to little ones. Age four is about the lower limit for me to teach, but I would consider teaching a three-year-old if they are really into it - and it sounds like your DD is!
With the littlest kids (3,4, and 5 year olds), I teach two kids at a time. We spend about 15-20 minutes at the piano, and another 15 minutes listening to music, singing, playing with flashcards, etc.
Most of what we do on the piano is rhythmic or creative - for instance, they play what a butterfly would sound like, or what an elephant would sound like. They also play simple songs on the black keys to start (easier for little ones to hit correctly). We also practice concepts such as high or low, soft or loud.
Away from the piano, we listen to music, and dance or draw, or make up stories about what is happening in the music.
All of this is designed to help the kids start thinking and feeling musically, so that when they are about 5 or 6, they are ready to start more formal piano instruction.
The reason I do it this way is that a lot of 4 or 5 year olds are put off by not receiving imedicate gratification. They are excited when they know that they can play something right away, without a lot of practice.
Suggestions I would have for your daughter might include starting lessons now (I couldn't tell if you were talking about her piano teacher or yours). I'm partial to the piano as a first instrument, because it is such an important skill, and it is very gratifying for children to be able to make music immedicately. But Suzuki string classes are also a good place to start.
Continue taking her to as many musical performances as possible.
Play music at home, and play games with it. Dance, make up stories, or draw what the music says to you. Don't worry about finding kid-specific music. Anything that is expressive, not overly complex and has a good beat is usually good.
Incorporate music into everything - have it playing in the car, sing or make up songs while you do activities or general chores (your creations can include "The Sandwich Song," "I'm Mopping the Floor," "Let's Get Dressed Today!" etc.).
I don't know if that's the type of suggestions you're looking for, or if you're already doing that stuff, but I hope that helps!
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