Can I run with my Yorkie ? I don't see why not. You may have to work up to it. Watch your dog for signs of discomfort or excessive panting. Your climate is fairly mild, but of course you know about watching temps.
My dogs love the fast walk, slow walk, speed power walk, rotation. My doctor tells me it is a better cardio work out, than jogging or flat out running. My joints wouldn't take the pounding anyway.