My deepest condolences. In our direct experience, the more open the situation and emotions can be, the better the healing will also be.
You don't say how old your DD is (or I missed it in the thread). We had to euthanize our big old guy when DD was 7 after a sudden illness (he was very elderly, but the end came suddenly). He was too large to help into the back of the SUV without hurting him (he topped 120 when he was a healthy adult). So we had the vet come to the house several times in the final days... including the final visit.
The last day we all spent with him, petting him and giving him one last wobbly walk in the sun. Feeding him chocolate (because, hey, why not) and yes, crying on each other's shoulders. It was hard, but it was good too, being there and feeling those feelings together. Our little young dog cuddled with him and gave him kisses.
When the vet came, we gave DD the option to stay in the room or excuse herself. She opted to stay, holding our little dog, and watch from the other side of the room. DH and I were hands on, with him through the end. Then DD donated her special yellow flowered sheet to wrap him in and the vet (who had a stretcher) helped us get him into the car for the trip to the humane society for final arrangements.
When I was about 7 myself, my parents had to put down our cat and sought to "protect" me from the trauma by not telling me or letting me see any sadness. They took her away to the vet and then were like "oh, sorry, she died." The result was that I was angry and confused and had no concept of how to feel. I didn't understand that she had feline leukemia and had to be put down. It was an issue with me for years afterward. They were doing what they thought was best, but I don't think it was a good decision.
We still miss our big old friend, talk about him fondly, and sometimes get sad. We have a picture of him on our "wall of ancestors." But DD has never seemed angry or confused about him or what happened. We are all at peace with it. And as a side result, our little dog has never gone looking for him or seemed confused by his absence, the way that you sometimes hear about.
So my recommendation is to be honest, be open, feel and show your feelings. Show her that a real man can cry when he's sad and that it's OK to be upset when you are loosing someone you love.
