I think it is difficult, though for people who really don't know how "black" someone has to be to be classified as black, rather than mixed race.
I would probably think someone looking like your dd would be mixed race, but I know quite a lot of people from varying cultures and races (e.g. white English, black African, Indian, Iranian, Chinese, mixed race white English/black Afro-Caribbean, etc).
For people who have more limited experience of "non-white" people, it can be a bit more difficult. Even my ds, who has very multicultural friends, said the following to me last year.
"Mummy, there is a new girl in our class, her name is "S"." So I said "Oh, great, what does she look like?" (Hoping to say hello to new girl and parents in playground). he said "Well, her skin is the same colour as "Y's" Y is black African (her parents are both from Zimbabwe). So next day I look for a new black girl in our area of the playground. Eventually I find a fairly pale brown girl, with darker skinned mother, and get chatting. Turns out "S" has a Jamaican mum and white British dad, and is not really the same colour as "Y". But to ds they are similar enough that he thinks they are the same colour. And he is no way racist, two of his best friends are from non-white families.
I would not have made that mistake myself. But not everyone is as observant, or thinks about things that much.
I know my mum (who is nearly 88) would have no idea - she just calls everyone who isn't completely white "coloured". You would think she would know better, seeing as two of her grandson's best friends are from Indian/Iranian families, but nooooo.........
I do try to educate her, but it is sometimes hard with older people who do not want to change their ideas.