I guess I've never considered that because she's off to Uppercross so quickly and we know who the sick person is there! ;-)
She doesn't seem ill in the first few chapters - a little low and very uncertain about the coming a particular person. I think I'd have to agree with Patricia about it just being the heat - the fact that Lady Russell won't be there soon (and honestly - would you want to send Anne to Bath with just Elizabeth and Mrs. Clay for company??;) - and the fact that LR knows for certain that Anne doesn't like Bath.