Former UPS employee here. I think dogs are primarily used on overnight shipping. It is more cost effective to bring a dog into an overnight sorting facility and position it in a location where hundreds of thousands of packages from around the country are going to pass by. Even at that, it is the government that brings in the dogs not the company (slows down operations) and it isn't used that often. But I still wouldn't do it.
Normally I would say that ground shipments are the way to go however, keep in mind that you have broadcast your criminal intentions to the world with your post and ya never know who might read it. It would not be hard to run a dog past every UPS trailer that enters Washington from southern California for the next few weeks.
Stick it in you pocket or in your underwear.