Older/elder daughter

I would not use either of them since you have nothing for a comparison. A mother is always older than her daughter.

Thanks for replying. I actually meant that if a person has more than one daughter, then how do you specifically describe the one who is elder/older of the others?

eldest / oldest

Either would be fine in your sentence.

So while introducing someone can we say, "She is Anna's oldest/eldest daughter"?

Thanks.

To me, Anna's older/elder daughter implies that Anna has two daughters. It doesn't seem odd. There are 229 results for "older daughter" and more than 50 results for "elder daughter" in COCA. I'm not entirely convinced that it's incorrect.

And here is an analogous example from two different English translations of the Bible (Luke 15:25):

“Now his older son was in the field, and as he came and drew near to the house, he heard music and dancing. (English Standard Version)

Now his elder son was in the field: and as he came and drew nigh to the house, he heard musick and dancing. (King James

ozzourtiTo me, Anna's older/elder daughter implies that Anna has two daughters.

Usually a comparative would be between two items being compared.
Anna's older sister is my younger sister's best friend.
But you are right that it's not incorrect, it's just odd to me.

There is nothing wrong with elder son/daughter/brother/sister. I think it better to avoid using older son/daughter/brother/sister.

If Anna has two daughters, the one who was born first is her older daughter or her elder daughter.
If Anna has more than two daughters, the one who was born first is her oldest daughter or her eldest daughter.

The superlative often stands in for the comparative in informal communication.