Gorget, correct. I couldn't think of the word. As for putting armor on the animal:
1)It probably won't survive anyways.
2) It would be much harder, I believe, to make armor for a small creature without impeding it's dexterity greatly.
3) The armor would be worth more than the animal. Warhorses were armored more for the riders benefit than the horses. He'd be dead if he fell in plate, he wouldn't be able to get up. For large, extremely expensive, exotic animals, maybe. But except for Jaqie Fox's Giant Toad killin' Kitten, no cat needs armor to kill rats.
4) It IS silly. The pictures you gave as examples are modern day novelty items for people who obsess about their pets. As for the example of a police dog wearing kevlar, it's not a "war dog". They sniff for drugs, tackle fleeing offenders, and whatnot they aren't meant for heavy combat.(Neither are the police for that matter.)Point being they have armor that:
a) is light. No contoured sheet of metal, doggie helmets and what-not.
b) is there because they are not meant to fight an attacker. They are not expendable, and not meant to sustain injuries, war animals are generally expected to so you don't have to. The horse being protected is to protect the rider, the animal is not a war animal the way a dog would be.
All that said, I'd support armor for appropriately exotic creatures, and for mounts. With the exotic creatures though, it should be very difficult to acquire and maintain. I remember seeing something about pet squabbles in the bloats saying disputes can be made when one pet eats another, that'll bring a whole new dimension to owning large aggresive creatures.
"Yer dragon ate me mule! And me wife and kid!!!"
(It'll also make you think twice about putting armor on them for when a dwarf attacks a pet that ate it's pet.)