Oh, I'm so sorry for your loss.................
Have you explained the concept of cremation to your little one? Kids are pretty cool about so many things, but cremaiton might be a bit much.
Ds was 4 when my darling mil died. She was cremated. Not saying you're going through the same thing, but cremation is cremation and a loved one is a loved one. Anyway, I explained that his Nana had died (he knew she had been sick). I said we wouldn't see her again, but that she would always be close in our hearts and that everytime we thought of her, she was with us because of it. We're not religious and I wasn't going to go into the whole heaven/angel thing.
Anyway, I explained she was going to be cremated, which meant that her body would be heated to a point it would be turned to dust. I think it was better than saying "burned" or put into an oven (too much Hansel & Gretel-like!!). I said that she wouldn't be a big person anymore, just a small bit of dust, even smaller than him! He found the idea interesting and was never upset.
Fast forward to this summer and my own Mom dying. Ds was now 13. He chose the 2 urns that her ashes were divided between. One (to be buried in my Dad's grave) was a lovely cobalt blue. The other is an Egyptian canopic jar (my Mom was passionate about ANYTHING to do with Egypt). That urn now sits on our living room bookcase. He feels comfort in having it near, and so do we! Some of her ashes we also put into a couple of necklaces, designed for such use (we got them from the funeral home).
You might want to buy a wooden (or, some other material) box and have your little one help decorate it, to hold the ashes. Pick a specail place for the ashes to be buried or, if you are going to spread them. I think children prefer knowing that something they love so much is in a place where they can put flowers or a stone memorial of some type.
I do think you need to explain the fact the dog will not be a dog anymore, before you pick it up. Would your child like to go to the crematory and help carry the ashes home. Being a part of things really helps them, as opposed to being excluded because the adutls think it would be too traumatic! Kids are amazing and are owed honesty.
I hope all goes well with your family. Again, I'm sorry for your loss......................