Depending on the size of the dog, I generally recommend a barbeque with a spit. Relatively slow cooking with frequent basting is generally best but you will need a pan underneath the spit to catch fat, etc. otherwise the barbeque ends up flaming up leaving a very unsavoury crust on the meat.
I often cook (also on the barby wrapped in aluminum foil) carrots, cubed potatoes, squash, and turnip, all slightly oiled and herbed.