I am so sorry you are going through this. Losing a pet, a family member, is traumatic. I wish you many good days of warm fur and waggy tail.
As non-christians/non-religious people, we don't talk in terms of heaven per se, but when our beloved dog, Tino, passed away from cancer in december 2010, we introduced the concept of "going to the sky" to our almost-3 year old. (We did not address the cat's passing when he was only 1). We didn't want to really go into the whole 'what happens to Tino's body now' thing, especially since we wanted to keep the spirit alive and our son is so literal he would not understand body as an empty vessel.
So very simply, we did tell him that Tino was very sick. Hard to miss as he was going through chemo and had a port on him, we spent time at the animal hospital, son had to be careful around the surgery boo-boos, etc. And we wanted to prepare him to say good-bye, even if the finality of it wasn't going to sink in until later.
We told him that doctors can help many, many things, but sometimes bodies were just too sick or too hurt. When that happens, people and animals go to the sky. There they feel better and are happy. It's a good thing, even though we miss them. They can never return to visit us because then they would go back to being sick and hurt. They stay there forever and we never forget them.
My son's birthday was just a few weeks after Tino officially went to the sky. One of his balloons escaped the house and when he saw it rising up to the clouds, he said is was ok because now Tino would get to see it and smile. My heart was simultaneously filled with joy and sorrow.
Now that my son is 4, he still refers to Tino being in the sky and equates someone being dead with being there. He has more knowledge of the body not literally rising because he has seen Tino's ashes, but still accepts that Tino can be fine there without it. Sometimes he sees a cloud and says that it is Tino. He used to get a little excited that we might see him when we're on an airplane but that has passed.
I found that it was ok to let him see us grieve and let him ask questions. As terrible as it was for us, it has turned into a good starting point on these larger issues of life and death.
The pet-lover's version of going to the sky is crossing the Rainbow Bridge. I love the idea of Tino (and the cat, Timothy, that hated him!) enjoying "life" with treats, frolicks and friends while they wait for me to join them. The poem about it and the visions in my head bring me peace. I hope they can do the same for you.