It is true that people can get AMS (Altitude Sickness) at 9000', but it would be very rare for it to be fatal at 9000'. Still, stairs will be a pain in the butt for a while.

If you (well, your neice in this case) have the time, aclimating is the way to go, although one could do it in a couple of days. When I climbed Mt. Whitney (14,501') a few years ago, I aclimated over two days without ill affect although three would have been better. When I climbed Taylor Pk (13,000' and some change) last summer, I aclimated over one day only. That was a bit rough since I left from sea level the day before, but I did all right. Note that everyone is different with altitude. Some get it at 10,000', some at 13,000', some at 17,000', etc. It depends on the person and the time allowed for acclimitization. Under 10,000', most people can adapt fairly quickly, although it'll be multiple weeks before they'll feel comfortable playing basketball or something.

A drop of altitude of as little as 1,000' is often enough to ameliorate atltitude sickness.