The best bushcraft dog? A Hälleforsare any time!
Can it kill a animal for you? It's a hunting dog and if it want it can kill anything that runs or flies, there is stories about some of them killing moose by them self... it's that enough meat for you?
How about protection? They are used as hunting dogs for moose, bear and wild boar so if you train them well they will protect you from anything but a atom bomb...
Stamina? One of our old dogs could if he got the scent after a moose run after it for a day and not come home after 2-3days...
Suited for the outdoors? They are a Spitz type of dog so cold weather and rain are nothing for their fur, the color of the fur is red or light yellow so you can easily see them.
If they are well trained they are the best you can get, if not why not try a Jämthund, Norwegian Elkhound, Karelian Bear Dog or a West Siberian Laika? (Note the last 2 are a bit aggressive to other dogs and people)
Since the Spitz type of dog is the one closest to Wolf genetically almost all Spitz type of are good bushcraft dogs.