And again I ask…why the Ivies? If your daughter is really interested in computer science…there are tons of other colleges with higher ranked computer science programs.
She is a strong student…there are many strong students applying to Ivies. Where else does your daughter plan to apply?
But back to your OP. Your daughter’s school counselor at her private high school likely has a good sense of where students like your daughter have been accepted. But if your daughter wants to apply to an Ivy then she can apply (assuming the school will send all the required materials). If she does or doesn’t get accepted, you will never know why. So…go for it if you’d like.
Does your daughter already have some sure things for acceptance and affordability that she like chosen for her college list? If not, I would strongly suggest she get these chosen FIRST. Build your list from the bottom up. Make sure you have two sure things that your kid likes and are affordable. Then find some schools where it’s likely she will get admitted. Then choose a some of those reach schools (like the Ivies). A balanced application list is important.
If your daughter can identify a school with rolling admissions that is nice because it sure feels good to have that first acceptance to a college a student really is happy about (I’ll suggest University of Pittsburgh).
I’m linking a thread I would suggest you read. It’s older but is a must read for any student who plans to apply only to elite schools. This student was a NMF, top in his class, excellent ECs and LOR…and no one expected he wouldn’t get accepted someplace but that is what happened. Read the whole thread, because it provides some very sage advice. Admissions have only gotten more competitive since the student in this thread first applied for admission in 2005. He did get accepted after a gap year, and to a terrific school…but his senior year spring and summer were not fun.