I understand that you will not be subject to the full body scanner with a dog. If you are chosen for the scanner with the dog, you will go through the WTMT with the dog and then you and your best friend would be subject to the full pat down. The carrier, sans dog, would go through the x-ray machine like they have in the past.
I found an article from Peter Greenberg on the subject:
Of course, as with all things having to do with the TSA, YMMV.