Nursing is permitted without limitation until age four. If the child is "weak" (a more lenient definition than ill), then nursing can continue until
age five. In the case of actual illness, then the rules of possible danger to life apply and an individual halachic decision may allow nursing longer if needed.
As you daughter's circumstances clearly at least reach the definition of "weak", you may continue nursing until age five. As she approaches her fifth birthday, we suggest discussing with your physicians (and possibly dietician), the role of breastmilk in her diet at that time. At that point, another halachic question should be asked.
There are no halachic guidelines about when and how to wean in this situation. Follow your intuition and slowly start cutting back feedings when you or your child are ready. Using small prizes, or cuddling while reading a book instead of nursing will help her adapt.
There is no difference in these halachot whether the child is a boy or a girl; the same rules apply.
We recommend asking friends/acquaintances in your neighborhood if there is a recommended local parenting class. You can also find lots of resources online for Jewish homeschoolers. There is even a Facebook group "Torah observant homeschoolers in Israel" that may be of interest to you.
Please feel free to get back to us with any further questions.
B'Hatzlacha and refuah shleimah!