Um does a pets treasures effect it in any way, is giving them certain things better than others??

Nope. Pet treasure is another way to personalize your pet c:

it's all up to you. i recently have been up to pet treasures, but i normally don't bother with them. /shrug my current pet i'm working on isn't getting a treasure, minion, nor anything else asides his very scary profile and the overlay to match.

If you collect Achievements, then there is one for having a pet with a big treasure chest.