Some will be your lens choice, some your camera and some your technique.....
This sort of photography is really demanding on any af systems. Not only are the dogs fast moving, but they are small targets too!
There are a few ways to get better results with your existing gear. One would be to pre-focus - such as on the post in shot 3 or a little behind it and use the burst mode to capture the dogs as they make their way through the exercise.
That said, I am not familiar with either of your lenses, however if I were to shot this type of event, I'd be looking for an AF-S 70-200, ideally the FL and if budget allowed, a D500 at minimum. I think the D750 should be able to keep up with the dogs, but you're going to need a reasonably fast lens and good technique to get these nailed.