I would definitely involve the vet with this daughter and get the benefit of the vet's experience. This can be a good thing, to be there when it happens. They can also plan a memorial of some kind. Depending on what they want to do, they can consider cremating the dog and burying the ashes - although this will have to wait until the spring. My neighbors planted a tree and the kids made a sort of plaque - one of those cement kits that you can decorate with little stones, and write the dog's name and birth/death years. Or they can have a little plaque made at a trophy place to hang on the tree. They can do the tree with or without the ashes. Depends on their religious beliefs. They should get good advice on the tree - they don't want to pick one out and have it die too. I would go to a good nursery for info. Some of them are still open, and no decision can be made before springtime anyway, so there will be time to consider options. This also helps spread out the mourning process, which is important. This is not something that most people can deal with instantly.
There are some great books on dealing with the death of a pet - your friend can talk to the librarian and get some ideas, and most libraries will help you borrow books from other libraries in the network so there is no cost involved.
Another thing to consider doing after the dog dies is seeing if there is a shelter that can use the dog's old items - many of them want old dog beds and toys for adopted/abandoned animals they take in. The daughter might want to collect old towels and blankets too - stuff that is too worn to be used by people can make a nice bed for a lonely dog. This can be comforting too, to know that their beloved dog's items have been passed on to a needy animal. Depending on the girl's age and personality, she might want to do a little neighborhood collection and help others clean out their linen closets while helping a shelter. Your friend can call some shelters now to find out the need, or just do it afterwards. But it something to think about so they don't just chuck out their dog's things - maybe box them up and then try to find an agency that needs them.
These can become very special times for families, and it's not a bad way for kids to learn about death. You are a good friend to help out.