I don't see what's so hard to accept or understand about the state of non-existence.
Me neither, EXCEPT when you have seen someone after they have "passed on". (I'm not even going to go there, let everyone believe what they want ... My belief: there definately is an afterlife.)
Re: Doggy Heaven .... haven't seen one of my numerous dogs since they've passed, but I believe higher life animals have "souls"... therefore, they too still exits (more so than some of the "soul-less" people I've known)
my 2 cents, based on experience