I agree, I do think Fanny expects to be treated different because she is a real sister but she also said:

What brother on earth would do half so much for his sisters, even if really his sisters! (Chapter 2)

I think Fanny’s selfishness would have driven her to talk JD out of helping even his real sisters. I bet Fanny did not share well as a child. Is this also a dig at brothers to flatter John about his Generous Spirit or was John really being extraordinary in his initial plans of giving his sisters 1,000 pounds apiece--Chapter 1. ;D