I would not say correct her, I would prefer to explain to her, in simple terms, that in this case the color has more meaning, as well as the moon may be the ball on the sky in one context, while in another context it is just the time span of 28-31 days, where the current values came from animosities of rules of some far country many centuries ago (months named after the rules and MY month cannot be shorter than his month).
Somebody would tell here soon anyway, better be it you in a nice and friendly environment, than some rude, who does not know better (and just got splinter of that information) and tells her "you are just wrong and therefore stupid and not white at all, if you are Asian" (or something more rude).
Going with the month parallel, I would agree, that her skin is nice white (and the ribbon goes really well to it), but as the word moon has more meanings and some have historical roots, which does not even matter now, "white" has also more meaning when connected to people, which have some historical roots, when in old times peole realized that some have white skin, some dark, some more yellow tones or red and came with simplification to call whole nations by colors, they had seen as different in majority, but does not have so much validity now, when anybody can marry anybody and there is oftentimes not a strict distinction, what exactly the supposed "color" even should be. Mainly if while her ancestry is from Asia, but her skin is a lot whiter, than of some people from, say, Europe. So that she is right that she is white as far as it goes for skin color, but there is also the ancestry, that her family comes from Asia, so she is also Asian.
And that is like if Ted's family came from Austin in Texas, so he is both American and Texan and Austrian at the same time and it is not conflict or problem. And Ava is from a family, which has roots in Africa and her skin is darker, but not so dark as the skin of (there must be somebody darker than Ava, if not in neighborhood, then on TV she sees).
And that she is white (as per skin tone) as Chloe, but that Chloe's family came from this state/city there and you're from that state/city so there are also small differences in that. As well as there are differences in hair color and eye color and that that she prefers different colors of robe/ribbon, than Chloe does. And that that all those differences of color do not matter so much, even if they exist.
(or something like that)
You cannot prevent her from the facts in the world, but you can explain her in the terms, that she would understand and not be ashamed when she is confronted with it, rather to be proud. "Yes, I am Asian and I an as white as Chloe, who's American and Hans, who is German. Some Americans are not even as white as I am. Why it should matter anyway?"
I am from Europe and at 3 I was aware, that in Africa live black people and that some children around have different colors and a different heritage. I did not care much at that time. I owned a lot of planets, where lived people and animals of all possible colors in harmony.
I remember, that around age 5 I did know some basics about that people are born, not that they are found under a rose or a crow brings them or so. My mother was pregnant and I knew, that there is my sister inside her, but the sister is just so small a baby, that she had to be protected by my mother's body all the time and that when she grew more, she would be able to came out and play with me and I would have to protect here. (well no technical details, how it is exactly done, but I do not care, it was natural, that it happens somehow at the right time. I was allowed to touch the tummy, she was inside, feel her move in there and sometimes kick, but I must be gently, to not hurt or scare her. Around age 6 I was allowed to carry my sister part of thw way home when she was finally born (well probably hard supervised by my parents, but I was the Prince, who has had a little Princess in his hands and was resposible for walking steady and holding her firmly on her first way home). I still remember, how I was disappointed, that she does not play with me and still cries and does not grow at all, even if I checked her like 5x a day)
So maybe it is hard to believe now, when your dauther is just 3, but in two years she may even hear something about how are child are born - you cannot pretend to her for long, until she gets some hints from other sources. So I think, it is better to be open with her, just on the level she needs to know about the world around - simple level, sure and not much details, but not lie to her and do not think she could not discover something until you explicitly allow her to as it does not work that way.
On the other hand, do not push much details and burden on her, answer her questions honestly, but with regards to her age, do not avoid difficult topics, but you need not go in too deep and force her to know and agree on the hard reality.
If you cannot totally shield her from reality, it is better to prepare her gently in a loving and safe environment to the parts of reality, which she is going to meet soon, than just deny it all and try to fix results, when damage is done. With a careful approach the damage may be prevented a she can accept it as all other oddities of world, she had to accept so far (why is mom so much larger than me? Well she is older so she had longer time to grow. But granny is not larger than father, even if she is older. Well no everyone grows equally fast and older people do not grow so much ... ok, it makes sense now, even if it's just small part of the really complex biological science).
So she is white, as well as Asian, as well as Princess of pony kingdom - it is all true now but more important is, that she lives in a loving family and is accepted as who she is without questions.
You are caring about her and that is important. She has a safe and loving home and that counts much more than that in the world around are some illogical or unpleasant things.