Hi Neil, welcome!
What type sensor are you using? Cropped, full frame? What type of pet shots? Shows, outdoor, indoor, close, far, lighting,etc? There are a number of factors to be considered. I shoot primarily full frame but also have a cropped sensor. Although I have several lenses, including a 70-200 f2.8 L IS, I find most of the time I use my 24-70 f2.8 L. Great focal length overall. The 70-200 has awesome brokeh and tac sharp but limited if shooting a cropped sensor.