Look for some kind of singing and music group such as Colourstrings kindergarten or Kindermusic. Anything Kodaly-based is a particularly good starting point for developing here listening and sense of pitch and rhythm. Then when she's a bit older she'll be in a good place to start learning an instrument.
Or if she's keen to do it, you could start her with Suzuki violin or piano straight away. I wouldn't rush the instrumental thing unless she wants to though.
Hi , she is only 4 so I think there is really no rush; but if she is musical and you specifically want to develop her musicality, I should think looking at more dance later on or perhaps other types of dance too, rhythmic gymnastics if she has the right build, music lessons or singing might all be good for her. I wouldn't start any of that so young but you will have to know what it is right for your own dc and see what is available where you live.
DD is 4.1 and her ballet teacher commented that she is "very musical". I too have noticed that she does move in time to different styles of music.
So my question is what other activities should I introduce her to to build on her flair for this kind of thing? I don't have any kind of musical background so am a bit clueless. She attends nursery and swimming lessons.