Personally, I'd have extreme reservations about it, given both the age thing, the allergy thing, and the overall culture of frats and sororities. That said, maybe she can check it out cautiously with the responsible friend from the lab at her side. Your DD has a good head on her shoulders and it's possible to likely that she'll want to get away without turning her back on the place.
College kids aren't exactly known for being tidy and careful about leaving food lying around, so it might be a good idea for her to quiz her friend about the amount of food left around the place (also might be enough to put her off joining).
Also, there's a difference between being a member of the group and living in a sorority house (I wouldn't go for that, BTW --- no way, not at all). Well, I'm assuming that not all the members live in the house?
Rush week: the sorority sisters would have to understand that forcing your daughter to do many or most of the inane things that get done during rush week and beyond can land them in jail and with a big civil judgment that will make their student loans look trivial.
They may treat her differently because of her age (meaning, anything from "sorry, you have to be 18 to join" to "we'll let you in without hazing but you can't come to the parties until you're 17 or 18.")
