I'm so sorry to hear of your loss. My husband and I have a 3 year old son. Since his birth, we've had 5 or 6 deaths in our families - all close family members: my father-in-law, grandmother-in-law, my grandfather, two of my husband's aunts...you get the picture.
Right or wrong, we've had him with us for each of the wakes and funerals we've attended. He's been great in every situation except one when I needed to leave the church service (for my father-in-law's funeral) because he just couldn't sit still any longer. Obviously, it's easier when the child is an infant, but we had 3 deaths in the last year which means our son was 2 or a little more...your daughter's age now.
We found that having him there helped EVERYONE! It was a wonderful distraction for grieving family - "someone close to us isn't with us anymore, but look at this wonderful blessing in our lives now!" That truly has been everyone's reactions.
I brought quiet toys/books for our son to play with, and let him play on the floor in the back of funeral home at the wake. there was always someone willing to watch him if I really needed my own time for grieving or needed to greet people. And even when he was a little louder than I wanted, the innocence of the questions seemed to comfort people (I know that sounds weird).
My biggest suggestion is this: do NOT tell your daughter that her great-grandmother is sleeping! We started saying that when our son asked what was wrong with (fill-in-the-blank) and then realized that he wasn't so crazy about going to sleep or having me and my husband go to sleep. Just tell her that great-gram when to see Jesus, or went to heaven, or went someplace very special...whatever you're comfortable with or your faith says.
I know this is lengthy and I apologize, but I've been there and want you to know that whatever you decide, it's YOUR decision. YOU AND YOUR HUSBAND need to be comfortable with whatever you decide. Don't worry about other people, worry about taking care of yourselves and your daughter and everything else will work itself out.
Let me know if there are any other questions you have. Again, I'm very sorry for your loss.