Your daughter is more than qualified for a top tier PhD program. The way most programs work is that she will do 3 rotations and take classes in year 1. After that, she will pick a lab and do another year of classes and research to formulate a thesis hypothesis.
The key is to find labs that she is interested in with space to accommodate students. Top labs working in the field of immunology might not have openings.
My humble suggestion is to look beyond what is “hot” now. While one cannot read tea leaves, the next hot area IMO will be tissue engineering.
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