P.M.
I believe it actually does children a disservice to treat death as if it's some secret too frightening to be endured. If your daughter is verbal enough, it's may help to introduce the idea of taking turns. Every person (animal, and plant) has a turn at living its life. When their turn is finished, they die so other people, animals, and plants can have their turn. For most of us, our turn is over when we are so old and sick that we aren't enjoying being alive any more.
But at her age, the finality of death won't be very meaningful. She will probably gradually forget Grandma except as recalled in family stories. The death will probably be far more emotional for you than for your little girl.
I would avoid associating death with sleep, because this makes some kids dread going to bed at night.
Hugs to you all.