Branwen, I have a son who has had glasses since he was three. It's definitely not too early to get vision checked, though it is true that kids vision continues to change through pre-school years. Ask the Dr on that one.
It's interesting that your DS wants to read so badly. I have heard that some of learning to read is social readiness, which correlates with the phenomena of more girls being early readers than boys. Both my sons actually resisted any kind of formal reading instruction until they could read. My DS15 never liked the phonics books. His first "book" that he read alone was Captain Underpants when he was six, and 3 months later he was reading all the Harry Potter books. My DS11 has always been less mature for his age. He had learned to "read" (sound out words) at school and we all knew it. He insisted that he couldn't read and it came out that he was afraid that if he could read we would stop reading books to him (by this time his older brother preferred to read alone). Like his brother, he didn't want to read until he could read whatever he wanted which didn't happen until 2nd grade.
That being said (my own story I know) I would definitely honor her desire and if things don't click, get her vision tested. (I might not tell the Dr that you're doing it because she can't read yet
