The fare difference isn't directly related to the time between original travel date and the date on which you make the change. The new fare is simply the then-current fare for travel on the new date (assuming that it's the outbound date that will need changing, as your post suggests). So if the day before the original flight, you move the outbound date to a date two months away, then you might still get O class availability on the new date, thus minimising the fare difference.

However, if at that stage you move the date by only a week, then you could be looking at a more significant fare difference - that's simply the same phenomenon as if you book a brand new ticket at short notice.

If she needs treatment, can you get an idea fairly quickly about how long that will last? Or will you need to wait until the first appointment?