If the metered area is truly filled with 50% of each, you can go with exactly what the meter says, and get an exposure that will most likely let you print the pic the way you want it. If you have a high contrast film like Pan F, you might want to give twice as much exposure. If you have a low contrast film like HP5 or Delta 3200, you might want to give half as much exposure and develop 25% more.
However, more technically speaking, the dog is not "truly" black or "truly" white. If you were to take a spot meter to each color (or get close with a wider meter), you would know exactly what the difference between them is. Probably not 10 stops, as it would be if they were "truly" black/white. Probably not even five stops, unless you are in bright direct light.
So, the "technical" answer(s), sans tonal placement: 1. meter a grey card in the same light as the dog, or 2. use an incident light meter. (This is equivalent to #1.)
But then again, this is usually one of the best options for any metering question, so no surprises here.
If I had time, I would place the black. I would meter just a black area and underexpose that reading by 2 stops if I wanted detail (or wanted to at least give myself the option of printing detail there later), and 3 stops if I just wanted texture, and knew for sure that that "texture" alone in the blacks was enough to get the print I envisioned.
Honestly, in practice, I'd just set an exposure for the overall lighting situation based on experience, and forget about the in-camera reflected meter, except perhaps as a rough self check. Catching the right moment and getting it in focus would be more of a concern/challenge than how to expose.