Im so sorry for your loss.
We had a similar situation a few years ago and I had to tell my children about it . We got advice from a children charity because I knew the children woudl ask how she died and I didn't know what to say .
They said to explain that that the person was dead, which means that they will never see them again. That the person was feeling very sad and mixed up ,they wanted to stop feeling so bad so they put something round their neck and pulled it tight and stopped breathing . When you stop breathing you die.
We were also advised to emphasise to the children that when you feel sad, angry and mixed up, you need to TALK to someone . This is not the way to handle mixed up feelings .
You also need to be prepared that your DD might ask factual questions about what happens to the body, burial / cremation etc.shes not asking this to be morbid,it's quite normal .
You need to let the school know in case she's upset , asks questions or even tell the other children .
Hope she's coping ok, glad to hear her dad is supportive and you are managing to keep up her clubs etc