I am a parent who has put three kids through college recently, two will graduate soon

...... one with a BS and one with a Masters! Sorry, it's been a long road and I just had to brag!
Have you toured the dorm where she will be staying? That always helps you see exactly what you are going to need.
The suggestion of a good basic first aid kit is perfect and a must!
The tool kit is also one of favorite things to make sure that the kids have and of course know how to use. One of the colleges one of children attended would not allow tools of any kind but all of the others did!
Another must in my book was a flashlight just in case of emergency. You never know when the power might fail or some weird critter sneaks in and gets under a bed or dresser. Our one DD ended up with a large snake loose in her dorm. It was a wild one, as in one that come in from the outdoors rather than one that some dorm mate had sneaked in as a pet!
The kids use to need a stack of quarters to run the laundry but it seems most colleges have wised up and included either laundry cards where you load on money or free laundry that is tied to the school ID. If the laundry room is in another building you may want to get her a hamper on wheels.
Schools have different rules about the use of extension cords and or power bars so you need to check the college's web site and see what is allowed.
We always packed a good mattress cover and pad. Most of the mattresses have seen some wear and tear and I just felt better knowing that the bed was covered. Our son liked to sleep on one of those egg shell pads so he packed one of those every year.
We use to send the kids with addressed and stamped envelopes but with the commonness of the computer we gave up expecting letters.
I think most kids today take a computer with them to college. All colleges have computer labs and in fact ours still use those for printing to save themselves the cost of ink.
One thing I have learned is to not allow them to take anything that is irreplaceable to college. DD lost/had stolen her favorite necklace. She was so upset but there was really not much to do about it. Things disappear so make sure those things are just that things! Expensive items can be marked with an engraving pen. We borrowed ours from our local police department. You can also check with your home owners policy and see if they cover dorm room content and what those limits are.
We were surprised when 2 out of 3 of our children asked to have us bring them a bike on our first visit to them. The learned quickly that many campuses are large and that a bike makes life easier. Now these two were in the south and I think the nice weather had a lot to do with that. Our other child was in college in the north and I suspect that the snow may have discouraged bike riding!

If they want a bike make sure you get a good, easy to use and compact bike lock.
All of our kids wanted good sturdy back packs. College books cost a literal fortune and weigh way too much!
We learned to hit
Walmart at home at the end of summer and stock up on spiral notebooks, paper and basic school supplies. It seemed by the time college started their local stores charge much more for these basic items.
Depending on your child preferences and hobbies you will have to pack some strange stuff. Our one DD loved to ice skate and found she missed her skates. Another child got into an outdoor adventure club and before we knew it she had acquired rock climbing gear with all kinds of ropes, helmet and beaners. She now has off campus housing and has an entire bedroom devoted to her and her housemates outdoor gear!
The kids have always packed (or purchased at the local store when we arrive), some of their favorite snack foods. All three kids ended up with refrigerators and microwaves in their rooms. It ended up being cheaper to buy them than rent them but then you do have to haul them around and store them over the summer and sometimes beyond that. You would laugh if you saw the mini frig tucked into a corner of one room in our house right now. DD did not need it this year as she is in a house but she remarked that you just never know where she might end up next year so please just store it for me!
Those summers home were the biggest adjustment for all of us. Beside trying to find a place to store their accumulated material goodies; you have a child who is now use to coming and going whenever they please. It took a few conversations on everyone part to remember to be respectful of others in the house.
All in all it has been an incredible experience for all of us. Try to just smile, relax and have a bit of fun. Oh yeah, sneak a box of tissues in the car for the ride home!

You will survive this!