An institution like that will almost certainly impart at least some of its values and beliefs into your daughter. This could cause far more damage to her in the long life than the prestige and 5% higher starting salary a Duke diploma could bring. There is still plenty of time to find a better university. Her values will be worth far more than her knowledge.
It depends on the kid. I went to a place that was very elite, and as Red as 0bama's diapers.
I thought I was a liberal when I got there. There were actual conservatives there, but I didn't know them. But in that environment, surrounded by Lefty geeks, I was criticized for quoting Thomas Jefferson. I realized that a liberal is a Communist talking his way into hell more slowly. I found that I was a conservative Democrat, at the least. Within a few years, I was a Reagan Republican.
It was going to a liberal college that taught me the panicky phoniness and logical emptiness of liberalism.