To be away with the fairies means to be out of touch with reality, which is what he thinks she may be.
Consider the statement ""I really wouldn't worry about going to work tomorrow," he says, reaching over and patting my knee, "I think she may be out of touch with reality."". Is the statement ""I really would'nt worry about going to work tomorrow," he says, reaching over and patting my knee, "I think she may be away with the fairies."" false? Yes/no/unknown