I'm just wondering, having read your post again, Batters, whether your daughter is linking colour with skin. She may have simply chosen two colours. I think scummymummy is right to stress the more serious implications of this, but if you talk to your daughter, a good starting point could be to ask her why thinks one mermaid is black and one is white. Just for the record, it took ages for my son to notice skin colours. And even when he was 5 or 6, whenever he described his friends to me, skin colour was way down the list.
And as others have said, I think it would be a good idea to have a chat with the nursery staff, so at the very least they are pre-warned that your daughter or other children at the nursery could come out with some inappropriate phrases.
Also, in talking to your daughter, stress how mean it is to refuse to play with a classmate, whatever words and names are used.