We did several dogs not too long ago, except we bought liquid nitrogen from the welding house. Got a cheap styrofoam cooler (like from a convience store) and cut a hole in the top just big enough for the brand to fit it. Pour some nitrogen in close the lid and put the brand down in the hole until it stops "boiling".
The key to the whole operation is to hold the brand on long enough. You'll need about four guys to help hold. We ran them probably close to 10 seconds.
Also be sure to shave the dog completely bare where you intend to brand.
That is exactly how we do cattle.
