Glad we're back on track.
At the risk of overstaying my welcome....
The difference for this thread vs generic sports/action shooting is that for Helen's purposes we are talking about her photographing her pet, Jasper. Within reason she can choose when to shoot, where to shoot, which way the dog is to run, the direction of the light relative to the dog, the weather conditions and so on. Clearly this is different to shooting at an event which is not under your control as a shoot and where the action could be taking place anywhere within a 360 degree circle and with all sorts of obstructions, canopy, whatever. It's also not the same as a sports shoot where you might have teams running in and out of harsh sun and heavy shade within a stadium or where the light is fading at either end of an indoor court or it's piddling down at night under floodlights.
But just as a studio photographer takes care to set things up to his/her liking - background, lighting, posing, props and so on - why shouldn't somebody shooting their own pet pay similar attention to the variables over which some choice can be exercised? Instead of just
taking photographs why not
make them. And picking days with nice lighting means you can achieve higher shutter speeds more easily without going mad on the ISO and that's only going to benefit IQ further. You also get shiny fur, sparkly eyes, improved microcontrast and more definition of features if the light is right.
e.g. with a fully sunlit scene and a slow (f/5.6) zoom lens you might choose to shoot at 1/1600, f/8, 400 ISO, which should give you a well rounded attack on subject blur, camera shake, focus error and noise. Pick a heavily overcast day in winter and you could easily lose four stops of light. That might drive you towards settings nearer 1/800, f/5.6, 1600 ISO, which I think is less desirable on the whole. If you have a faster zoom lens (f/2.8 or even f/4), or a decent prime then your options expand.
Just as an example of the difference lighting makes I have a beach scene shot a few years ago, one day in overcast conditions and one day in bright sunshine. The difference in appearance and emotional response is, I think, striking. One photo makes me want to be there. The other really does not.
That's why, when it's for my own personal pleasure and in a timeframe I set for myself, I make a conscious decision about the type of lighting I prefer for that shoot. If it's a TP meetup or other scheduled event then that decision is taken away from me, although I have pulled out of meetups when I've felt the light/conditions were far from ideal.
Anyway, back to running dogs....
When I shoot my dog I will usually have my partner with me, the sun (or bright sky) over my shoulder, and she'll go 20-50 meters ahead of me and then lob a tennis ball back in my direction. The dog chases it and runs (usually) in a fairly straight line towards me and I have a chance to rattle off a series of shots as the dog approaches. Instead of shots of bums and backs of heads I get a nice shot of the face, hopefully with a shine in the eyes and some depth and definition to the face/body/fur. With my drive mode set to high speed I may even have the fortune to capture a nice pose. It usually takes a few runs before I get something I'm happy with and far more shots go to the bin than are kept.
As for focus modes, for Canon it's going to be AI
Servo (never AI Focus!) and beyond that the choices are dependent on the exact camera model and its capabilities. Centre point is the safest bet for most cameras and if you want a more imaginative composition it might be better to shoot a little loose and then crop to taste. More advanced cameras will offer more options. I'm not sure about the 600D, but I would think that centre point only would be the best point to choose by far.
Probably the most difficult thing, at least in my experience, is to keep that AF point aimed where it needs to be - right on the dog's face - and that's tough if your dog has a bouncy gait. Practice helps no end.
Just for a change of angle (but still with light in the eye)....
1D3, 400mm, 1/1250, f/5.6, 400 ISO
and a change of pace....
1D3, 400mm, 1/1000, f/8, 400 ISO
but still I like to keep the shutter speed up.