I'm worried about my 4 year old daughter's bereavement issues?

This is a stage of learning to cope with it. She's play-acting the situation that scared her. Also she's playing funeral, which is also pretty normal. Especially the very young child play-acts through these things in order to work through their emotions about what happened. You should be able to call the doctors and ask for their advice, but to me this would be pretty normal and I would see it as a step to her finally accepting that Jemima is gone. It's perfectly normal and I wouldn't be concerned.