I've just had a fixed brace put on, it cost over �2500, this was for ceramic brackets - clear ones (google this if you don't know what they are), and the metal ones were �150 cheaper, unless you go by the NHS, where you can have metal ones for free, but not ceramic ones..
Because I'm 18 I had to go privately, I don't know if this is just my orthodontist or all, but I'm still in full time education and that made no difference. A dentist is different to an orthodontist, so as enigma said, she may be entitled to free dental work as she has a child under 1 year, however this may not be the case for her orthodontist.
As you said you don't think she needs a brace.. well I didn't think I needed one, I've got a great dental record, all my teeth are pretty much straight, I just have one baby tooth that hasn't come out, so I need to wear a brace for 2 years, have the baby tooth extracted, and the adult pulled down with the brace!!
Her teeth may look like there's nothing wrong with them, but alot of the problems lay in the gums.
Hope this helps :D
Lou xx