Armor proficiency is more want than need.
Animals are normally not proficient with armor. As per PRD Armor Proficiency feat:
Normal: A character who is wearing armor with which he is not proficient applies its armor check penalty to attack rolls and to all skill checks that involve moving.
Usually only light armor (leather or masterwork studded leather, mithral kikko) is worn with no proficiency, but it is up to you to decide if the benefit of having more armor outweights the cost of armor check penalties. For example, a Mithral Full Plate has armor bonus +9 and armor check penalty -3. In Pathfinder, you can spend three feats to get Light Armor Proficiency, Medium Armor Proficiency and then Heavy Armor Proficiency to limit applicability of this penalty, but you do not have to.
Masterwork cost is added after everything else.
So, for a large quadruped, the cost of armor is:
final_cost = base_cost * 4 + 150gp (this gets a bit tricky when you consider special materials, which have masterwork cost built-in, but reverse-engineering works).