Hi, John and welcome!
Of the items you mentioned, a few may help your daughter get through TSA screening without a problem: her driver's license permit without photo and her school ID with photo. She can also show the birth certificate. These would require 'additional' screening, which takes longer, so it's advised to arrive at the airport 2 hours earlier than you normally would. The TSA has databases they can check, with information your daughter may have to fill out on a form, plus, show these aforementioned items, to prove her identify and allow her to board the plane.
However, I have a few other suggestions that might be more helpful: have your daughter get a State ID with photo, from your local DMV and she can use this as her official photo ID; she can try to apply for and get, a renewed passport at an official agency that specializes in 'rush' passports (usually costs more), or she can try to move her driver's license test up, from the date she already has the appointment, if at all possible; then she should get the license on the spot, and that can be her main and preferred form of photo ID.
Curiously enough, a birth certificate and a social security card are not considered official forms of ID for traveling (TSA) and neither are the other items you mentioned. You can see the TSA's official list of acceptable ID's at the site below:
Scroll all the way down, for information about additional screening, in the absence of an acceptable form of ID.
At this point, I'd concentrate on your daughter getting the official state ID with photo, from any local Dept. of Motor Vehicles. Call them first, to make sure you get it that same day and don't have to wait for it to be mailed. That's how it works in my state--you get it on the spot, after you fill out the forms, pay the fee (usually small) and your picture is taken.
I hope you found my suggestions helpful and all will go well with your daughter's trip! Congrats to you both for her getting into UC Davis--a wonderful school!
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