I hope Google can put OIS for anti-shake and a good camera in there. You're probably going to need as good image stabilizer as possible, as you'll be moving and shaking (when walking) your head a lot more than with a phone that you can still keep more or less still.
I don't think optical stabilization would really do much for full-on head bobbing. It's more for finer-grained movements, like hands shaking. And I don't think our heads actually shake much.
That said, you could do digital stabilization on head bobbing and probably get a pretty good result by jacking up the size of the stabilization window, although you'd lose frame size.
