Hi Melissa,
7 labs is a housefull! They don't take up quite as much space as my Rotties but it's close. Show candids come in two flavors: outside where you can use pretty much any good lens; inside where you'll only be able to get decent pictures with fast lenses and you'll be shooting them wide open at high ISOs.
To get moving shots, you'll need a camera with high frames-per-second shooting ability and decent buffer depth. I'm currently shooting those types of activities with a Canon 30D and 40D. The 40D shoots 6.5 fps for up to 75 jpegs and 20 RAW files which I find adequate to get good moving shots. Faster would be better and one of the ID cameras might do a better job but the 30D/40D cameras are a good balance for both candids and show formals which I also shoot. I'm not a Nikon guy right now but you can look at the specs on the cameras you mentioned and find a good parallel.
As for glass, Jim Poor mentioned fast primes as well as a fast zoom and he's right on the money. Outdoors, my 70-200 F4L is a great lens and I use it for 90% of my ring candids but indoors, I use an 85 F1.8, 50 F1.4 and 135 F2.0 almost exclusively although I'll use my 17-55 F2.8 in the Group Ring. Using the primes means I have to zoom with my feet a lot but I like to move around with the dogs anyway so indoors, that's not a problem. Indoors, I'm always shooting at ISO 800 or faster. And even with the combination of fast glass and high ISO, I still get some movement of the feet on my action shots. If you're shooting black labs indoors, plan to push your ISO even higher and figure out how to deal with lots of noise in your images. The one basic truism of indoor ring candids is: black dogs + low light = blurry blobs

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For recreational shooting -- wildlife, landscapes, fine art stuff -- my 5D gets more action but I don't need the speed as much and can take my time to set up on a tripod and actually think about what I'm trying to capture. In the studio, I use both the 5D and the 40D depending on whether I'm shooting people, animals or both.
Good luck with your choices and don't forget that you can rent some gear before you buy to make sure it will meet your needs before you actually invest the in the camera/lenses.
Jim