I've thought about this quite a bit since it was posted. I'm not religious and I don't believe in the idea of heaven of the scriptures. Yet, like katdad said, energy cannot be destroyed, only converted.
zuma, you seem to understand the spiritual aspect of these things perfectly.
For most Judaeo/Christian people, most don't really believe in a bearded, white-haired and very Anglo-appearing Renaissance-style God wearing a white robe. They more intellectually understand that this is only symbolic.
Likewise, most scientifically trained people (I know this -- my degree is in chemistry, plenty of physics) still "imagine" the atom as a miniature solar system, the electrons orbiting the nucleus like planets around a sun. When in fact electrons are a probability wave. The "solar system" analogy is just a handy meme.
It seems that your spiritual concept of an "afterlife" is similar, a logical and conceptual aspect.
There certainly aren't angels sitting around on clouds playing harps in "heaven" -- nothing could be more boring -- but if such a place is possible for our earth-bound minds to grasp, it's instead a perfection of what we have here, all pain and anguish taken away, and so on.
My point being this... belief in a spiritual "afterlife" does not need to be predicated upon mythological concepts of a stormy, super-santa god (or Valhalla w. swords and battle, ha ha) as the basis. Instead a solid concept of a burgeoning and extended spiritual existence.
And that certainly allows and I'd guess ensures the concomitant continued existence of our beloved pets as well.
To do otherwise would (as I see it) violate the principles of energy (souls and spirits being made of pure energy) disappearing, when in fact energy can only be transmuted and transformed, not destroyed. This is a fact of physics. And that transmutation of our (and our pets') spiritual energy into something more pure and transcendent is very understandable and quite possible, even for those, such as you, who may not be very "mainstream" religious.
Bottom line, yes, our beloved pets continue forward. At least that's how I see it.