Provided you only want to shoot at outdoor events, the 70-200 f4 should be adequate. There may be times, heavy cloud cover, that you would prefer to have the f2.8 to allow fast enough shutter speeds to freeze the legs and paws if you want them to not be blurred.

7D Servo AF should be up to the job. Hardest part is keeping the active focus point where you want it on a bouncing target while also watching the framing and adjusting zoom to keep up with changes in subject distance. Can be hard enough with runners until you get used to it, let alone a smaller faster target. Seems to me that there is at least one reviewer of camera bodies that has used running dogs to test the Servo abilities. It is a challenge for both camera and photographer.

As far as the f2.8 goes, I'd suggest that you start with it in the first place if you can possibly swing it. It will save you money in the long run as there will come a day when you will, not might, be buying it for the wider aperture.