It depends on how much cooking your dd wants to do. I cook "proper" meals for myself most of the time at uni, so I have two saucepans, a small frying pan, chopping board, sharp knife, bread knife, wooden spoon, kitchen scissors (not essential, make certain tasks easier as a dyspraxic), serving spoon, casserole dish, pyrex jug, 2 plates, 2 bowls (useful when I have visitors), 2 glasses, 2 mugs, grater, foil baking trays for brownies and flapjacks, and, for some unknown reason, 2 eggcups. Some people eat catered food, some live on cereal and chicken nuggets cooked on foil. Most are somewhere in between, and those that cook quite often share resources between themselves (e.g. I borrow my friend's garlic crusher, she borrows my grater). One of my international friends used the communal saucepan and frying pan plus borrowing our stuff for the whole of first year, but they weren't as fussed about how clean it was. In first year I kept all my stuff in my room because about 30 people had access to the kitchen, although nowhere that many actually used it on a regular basis.
What was really helpful was a fully stocked store cupboard from DPs, with pasta, rice, couscous, onions, potatoes, cereal, a variety of tinned fish, fruit, and veg, curry powder and chilli flakes, and in my first term, a couple of those John West tuna salad things and couscous pots. That meant I always had something to eat even if I hadn't managed to shop. For my first term DM also gave me a full week's shop of fresh stuff, but I didn't actually use it all because of the amount of free food -pizza- available in fresher's week. Now I prefer to get bread, cheese, milk and fruit when I arrive, eat in Hall for dinner for the first few days while I'm doing exams, then do a full shop at the weekend.
Apart from that: the usual clothes, towels, books, a few photos maybe, flip flops for the shower. At the start it's handy to have a first aid kit and a toiletries kit made up, of course your DD can buy stuff for herself but it's nice to do that if you have space, or get some stuff on move in day, so when she hacks her finger making a fancy dress costume on day three she has plasters and bandages!
It's all quite expensive though, so you have to consider whether all this kitting out comes out of your money or your dd's loan/ part time job money - or if you do it as a going-away present, establish whether that's expected every year.