Hi, I'd like to help you with your question.
It sounds like you are doing an excellent job already. Listening, hugging and encouraging her to express herself are all great ways to help her feel open to expressing her grief. Being there for her is the best thing you can do.
Since she has to deal with this while at camp, she may need more time alone to grieve. Being around others may give her more time to be distracted and also more friends to talk to, but time alone is also important.
Another thing to be aware of are the stages of grief, which you may have already read about. Your daughter (and the rest of the family) will need to work through the stages until she feels she can accept her grandmother's death. Here are the stages of grief to help you recognize them with your daughter:
Denial- happens when we first learn of a loss. The feelings are so overwhelming that we block them out to protect ourselves emotionally until we have time to adjust.
Anger- occurs when we being to realize what has happened. The feelings are overwhelming and hard to cope with so we turn them around and try to find an outside source to blame. It can be the doctor who told us our loved one died or a relative or friend. We blame so we can deal with a loss that has no explanation. We try to find a source that can be faulted so we have something to focus on.
Bargaining- when we feel vulnerable from our loss, we try to find ways to gain control again. We do this by trying to bargain our way out of the loss. Making deals with God, saying you'll be good so the situation will change. These things are ways to try to make the loss seemingly in our control
Depression- any loss can cause depression. Sadness, crying, loss of appetite, and trouble sleeping are common. This is when we begin to accept the loss and the reality of it hits us. The danger is when we feel so bad we want to hurt ourselves. Then professional help is needed.
Acceptance- this is when we are able to accept the loss and we start to deal with it. It is not about being happy about the loss, but more an accepting and calmness about it.
Your daughter may skip some of these or go through all of them. With the amount of support you are giving her, she may not have some of these stages longer than a day or two.
With a happy occasion being celebrated during your grieving time, it is understandable that you would not feel as happy or express joy. It is more than appropriate if you are subdued and quiet. Saying you are happy for the person and providing a gift is good, and maybe socializing for a while. But everyone understands if you are not able to meet the normal obligations. Grief is primary right now and taking care of yourself and your family is understood by everyone.
Keep doing what you are already doing for your daughter. Be aware of the stages of grief and any signs that she is not handling her grief normally. If she would become deeply depressed or anxious, taking her for therapy to help her work through this would help.
Let me know if I can help any further,