Dogs are like people. There are the loud ones, the quiet ones, the social ones and the shy ones. Your grandma's dog might just be a shy, quiet dog. It might also just not be accustomed to barking, seeing as it's still rather young. Maybe as it grows older, it'll encounter more dogs and start the socializing process - afterall, a dog needs to learn how to interact with other dogs.
You'll sometimes see dogs that don't know how to interact with other dogs at the park - they'll be the ones that will sort of run up to a group of dogs, start sniffing around and then when the other dogs sniff back, they'll kinda run away back to their owner.
It's interesting to watch the way dog psychology works, and how they interact. It's even more interesting to do so when you know some of the backgrounds of the various dogs by speaking with their respective owners. I encourage you give it a try the next time you're at the dog park and see what you can learn about your (or in this case your grandma's) dog's personality around others.
