Tips on keeping moving subject in focus?

Pre-focussing is a good idea, a lot depends on the speed of your focussing system if you are going to rely on capturing without pre focussing.

I personally use spot metering in such situations and set the camera mode to S, so that I can concentrate on releasing the shutter at the right moment with fast moving objects. At least with using spot metering I can set the focus point on the eye of the subject (or whatever is relevant if it is an inanimate subject like a car or an aircraft).

The shutter speed will depend on the subject but 800-2000+ may be applicable especially if the subject is powered. (unlikely with your dog)