There are loads of things your daughter can do! My 12yo is keen on volunteering. Here are some of the things she has done over the last few years.
There's a soup kitchen which has a rota of volunteers to prepare food in advance at home (sandwiches and soup) and then bring it in on the day. It was my name on the rota but dd did most of the work. Although the official policy was that she couldn't help on their premises, in fact when we brought the food in nobody objected to her helping serve and clear up, so long as she didn't go into the kitchen.
Somebody round the corner from us collects items for homeless people: warm clothes, sleeping bags, Thermos flasks, woolly hats etc. We enjoy going round the car boot sales and dd has a small weekly budget to spend on these things. She likes getting the best value for money she can.
She did a bake sale outside our house and sent the money to the RSPCA. She has also sold her unwanted toys and sent the money to charities. Sometimes she makes craft things and donates them to charity sales. Just rounding up her friends' and neighbours' unwanted items and delivering them to the local charity shop is helpful. You could make up Christmas boxes to give to local homeless people or boxes of toys to send to children abroad - probably a bit late for this year but maybe next year.
She sometimes helps by playing with younger children in their own homes as a sort of volunteer mothers help to give their mums a break. This is done informally - just friends and acquaintances we know who are struggling to cope for various reasons. She also fetches milk and newspapers from the shop for two of the elderly people on our street. Occasionally she likes to cook our family meal and prefers to make something like stew or lasagna which can be shared easily with neighbours who find it difficult to cook their own hot meals. These are the things I like best, because it underlines the fact that you don't have to go through an organisation if you want to help people; you can just look around and offer help where you think it might be needed.
We used to help pick up and deliver library books for housebound people and dd ended up doing this on her own quite often - it was my name down to do it officially but the librarians knew she was responsible and no one ever questioned her doing it. You could volunteer as a befriender to elderly people in your area; we never tried that but I should think they might enjoy the company of a young person.
Sponsored swims, walks etc don't usually have a minimum age and if they do, it may be overlooked.
That sounds a lot but has been done over several years and not all at once. Probably my dd has a lot more time on her hands than yours does because she doesn't go to school, but even if your daughter just fits in a few things a year she might enjoy it.
If you are hitting a brick wall with larger organisations allowing your dd to volunteer, try small local ones. Perhaps they "should" have policies on health & safety and child protection which would bar your dd from participating, but they usually don't bother. So long as you, the parent, are happy that it is safe for her to undertake the activity then I think that is the important thing.