I can only comment from my personal experience.
I was a very late starter. I couldn't read at all until I was 7, nearly 8, by which time the school had sent various educational psychologists etc etc, and I had done badly with all of them.
I don't have a very clear recollection of this, but I do remember people coming and asking me daft questions: "In the picture, which car is the biggest?", and me thinking they must be trick questions so giving weird answers... I also remember learning all the songs for a school concert off by heart so that I could pretend to be reading the words like everyone else.
For me, things suddenly clicked. I don't remember it happening, but one morning I coudl read. After that, I was average, and then suddenly aged about 13/14, I became aware that I was above average and won a scholarship to a private school.
I went to Oxford for my undergraduate degree, then did a Masters at Cambridge. I'm now about 6 weeks off submitting my PhD, although I still can't shake the feeling that it's going to fail....! Old habits die hard!
None of this demonstrates anything, other than to prove that your daughter is not alone. I think things were probably easier for me as I wasn't really aware of anything at the time and it is only looking back that I can see how different things could have been.
Really good luck to her! - and I would encourage anybody to apply to Oxbridge, as they really do take all types and you won't know unless you try.