While this answer may seem woefully inadequate, and far too convoluted as compared to the comments already offered, I provide my own two cents.
In my opinion either option (c) or option (d) would've 'sounded right' – not a definitive scale to compare with, of course, but I admit with some embarrassment it is the one I use the most.
Considering, Superlatives and Comparatives, though, the option (c) proves appropriate.
While both sup. and comp. – I hope you pardon the abbreviations – are forms of adverbs or adjectives used for comparison, a Superlative is used to show performance ( in adverbs ) or quality ( in adjectives ) of the greatest or least degree.
- Amongst the boys, James is the tallest.
- Jack is the best pick for class prefect.
You will note, of course, the addition of the suffix '-est'. When the word has more than one syllables, you add 'most', 'least', or a derivative before it.
Comparatives, meanwhile, are restricted two merely two things.
- James is taller than Harry.
- Jack is a better pick for class prefect than Tom.
Again, same rules apply, only, the suffix here is '-er,' or you place 'more / less' before.
None of this answers your question, though. Regardless, it was essential to set the base, so that I can proceed further.
The above knocks down our options to only two, either (a) or (c).
Now, you may have noticed that I used for both superlatives the article the, but did not bother to do so for comparatives – wherein I had to provide another name for it to become two things.
This is because, when it is a single syllable adjective/adverb-turned-Superlative, we typically write 'the' prior to it.
This is also why I suggested option (d) as a contender. While I do not exactly know why we do so, I can offer numerous examples below:
These are, due to convenience, from Jane Austen, for which I hope you will not judge me – did what I could.
Northanger Abbey, Chapter 4:
The whole being explained, many obliging things were said by the Miss Thorpes of their wish of being better acquainted with her; of being considered as already friends, through the friendship of their brothers, etc., which Catherine heard with pleasure, and answered with all the pretty expressions she could command; and, as the first proof of amity, she was soon invited to accept an arm of the eldest Miss Thorpe, and take a turn with her about the room.
Northanger Abbey, Chapter 9:
Charles Hayter was the eldest of all the cousins, and a very amiable, pleasing young man, between whom and Henrietta there had been a considerable appearance of attachment previous to Captain Wentworth's introduction.
Above, you could accuse me of nitpicking, but 'an eldest' clearly won't go in your own question.
Now, I will be very frank with you. The only reason why I fell (a) incorrect is because of the rather puerile 'it does not sound right,' and examples that I have from my research. Most of the books I have searched this for only used 'elder' without a 'the' when they – and yes, I fully realise how bewildering it is to read that sentence – have a 'my', 'her', 'his', etc ahead as an attribute adjective.
To make it simpler, unless and until it was:
- This is my elder brother,
- He is her elder brother,
- She is his elder sister, etc.,
it always had a 'the,' or was converted into a sup. as in the case of
Even War and Peace by Leo Tolstoy has this; 'With her elder sister I was stricter.'
Now, for the examples I had promised above:
'The Mourning Brothers' from Ambrose Bierce's Fantastic Fables:
So when the Old Man was dead each of the youths put a weed upon his hat and wore it until he was himself old, when, seeing that neither would give in, they agreed that the younger should leave off his weeds and the elder give him half of the estate.
From Charles Dickens' A Tale Of Two Cities, Chapter X, I present:
'To distinguish the brothers, I will call them the elder and the younger; by the elder, I mean him who exercised the most authority. It was the elder who replied, `Since about this hour last night.'
Hence, and because "Of my two daughters she is the elder" sounds better than the alternative, "Of my two daughters she is elder," I present my argument.