You can grab one on test center but if you plan to do this, you might want to train one up on your production shard to GM skill levels then transfer over.
This would make your testing more realistic and you wouldn't have to train one twice.
Try out Wrestling Mastery. This seems like a good choice for non casting pets.
Once you start leveling it, I think you'll need an amount of taming and lore above what you could get from jewelry, but you can also vet this out on Test Center.
I've been experimenting with something similar, with the Anniversary horses. I'm still trying to come up with a template for a 3 slot pet that I will have a purpose for and plan to post the outcomes when I have them.