The TL;DR is "Nope, this is well within the realm of what I'd call healthy." I'm no psychologist, just an observer of the human condition, so take my observation for what it is.
Now, is that bad? Is it bad that losing my grandparents didn't affect me? Should one be unconditionally affected by the loss of one's close family member?
Your dog was obviously a close family member, and from the sounds of it, you were closer to your dog than you were to your grandparents. No shame in that. So you're obviously going to feel that loss a lot more keenly. I've been through the grieving process a few times, and one thing I've noted is that grieving isn't primarily about the person who is gone. It's about the person who remains, and the loss that they feel.
My grandmother died in 2005. We were very close. In fact, she raised me. I sat with her other children at the funeral, not with the grandchildren, because I was effectively her fifth child. It hit me pretty badly. So badly that I wanted to punch the next person who told me "She's in a better place now." And that's when I realized what grief for the dead was all about. I wasn't grieving because something terrible happened to my grandmother. It had, but wherever she is now, it's no loss to her. The loss was mine. One of the centers of my universe was now gone. The two things that helped me most were my little brother getting me massively drunk, making me laugh, letting me cry, and my mother telling me that "She's gone, but we're still here for you."
Fastforward about 3 and a half years. My mother died of pancreatic cancer, two days after Christmas of 2008. They took her off of life support a week before she died. During that week, we always tried to have at least one or two family members present with her at all times. We did rotations during the vigil. She passed early on Saturday morning. Her immediate family (including me) gathered to say our final farewells. When I went home that day, I felt what I can only describe as a sense of great relief. I went to bed and had several hours of deep, solid sleep.
My mother and I were ... complicated, to say the least. We could be very close at times, and then we could go years without speaking to one another. At that point, I was asking myself similar questions to the ones you're "Am I fucked in the head? Why am I feeling like this?" For me, the emotion was relief, rather than being unaffected.
Fast-forward six months, and the grief finally hit. It hit with full force too. This was about the time I started suffering from depression and constant thoughts of suicide. I got through the grieving process, but the depression remained. It took me much longer to get over my mother's death than it did to get over my grandmother's passing, even though I was closer to my grandmother. The reason? There was sort of a closure with the first and not with the second.
So what am I trying to say here? How we process loss is complicated. One size does not fit all. Emotions are ... for lack of a better word, weird. We can't just turn them on and off like flipping a light switch.
I'll end by saying that simply asking the question "Am I fucked in the head?" is one positive indicator that you aren't.