Hi Neil and welcome,
Bob has covered this subject very well but I'll just add a couple of additional points of view. For available light, outdoor pet portraits, you have to consider whether or not you'll be shooting off a tripod or hand-held. If you're shooting hand-held and you do your own baiting, you might want to consider an IS lens -- or the equivalent of you're not shooting Canon. This will make it easier to hand-hold with your right hand only as you toss a toy with your left.

For a starter kit, I like the 24-105 F4L IS and the 70-200 F4L IS. Both are excellent lenses in terms of image quality and both are plenty fast enough for outdoor AL photography. Also, both work on crop bodies as well as full-frame.

The 580 EX makes a great flash unit for fill light outdoors. At high-speed synch, it can be used at any shutter speed. The diffusers Bob mentions are excellent.

If your main focus is portraits rather than candids of the dogs in motion, I'd opt first for the medium-range zoom. It saves a lot of steps to be able to zoom with the lens rather than your feet. Image quality is almost as good as with primes. Again, if you are shooting Canon, pick up the $70 50mm F1.8. It's fast, cheap, and has outstanding IQ for the price and, on a crop body, it's a classic portrait focal length. I've found it invaluable both outside and in the studio for portrait shoots where I want to throw the background out of focus.

Good luck and let us know what you decide. And share some of your images. We'd love to see how you do.

Jim