+1 on Jim's advice on lighting. I also use bee's. I also use my 580ex II with a softbox but I will say I find pet's more intimidated by the large camera with bracket and softbox than the studio lights. Typically I'll just use umbrellas with my B400's. Under the right circumstances I will use a B1600 with a 48" octabox. Another thing to consider that I would highly recommend is a 5 in 1 reflector. Even if you are alone have the get parent give you a hand, reflectors are amazing and can really light up a dark subject, even indoor using window light, keeps the pet parent busy and out of your way as well.
One thing to be careful of. When forced to shoot high ISO and then use a tool like noise ninja, although the tool is great, with pets you typically want fine detail like hair and those tools can really over soften. I use noise ninja but seldom on pet shots.
Another benefit of the lights is they will freeze action. If you shoot outdoors and your budget allows, also think about Paul Buff's Vegabond II. I have one and it is awesome for locations with no power. The cybercync's are awesome as well. If you decide to buy bee's, I would recommend B800's over the B400's. Little difference in rice and twice the power. Start with one light and an umbrella and remotes and you have a reasonable priced quality solution, and very portable. Conquer using one light and then buy more one at a time.