They had 'old pig' on playschool a while ago - it's not religious. But it does have the general idea of I've done lots of things and seen lots of things and loved lots of things and now i'm dying - so it may not work for explaining "unexpected" death.
You may also find that your DD forgets a lot that her teacher has died - it took my DS many months to understand that he wasn't going to be able to talk to or play with or phone my Dads partner after her death. And he still occasionally suggests going to visit her.