Where do I pick up this awesome looking armor for Dogmeat in Fallout 4?
That's Dog Armor. Sometimes attack dogs will have armor on them, which can be looted from the dog's corpse. There are multiple types. The dogs are usually found with Raiders.
In addition to the armor, Dogmeat is also wearing a Dog Helmet. I have yet to see a dog helmet in any of my playthroughs, so I think they're less common.
Neither the armor nor the helmet provide any damage reduction, but they do both have weight.
According to the Fallout Wiki page on Dog Armor:
South-East of Walden Pond you can find a small cave guarded by 3 Mongrels. Scattered across this cave you can find Dog armor, a Dog helmet and a Chain dog collar.