Hi everybody, thank you much for your great opinions. This is helping me greatly. I'm reading your comments. Is it a bad idea for me to get a D40 and a Nikkor 70-200mm f/2.8G ED-IF AF-S VR lens on it? This idea came to me because:
1) You say "the camera isn't as important as the lens"
2) I tend to be away (5+ feet) from the dogs at the field
3) Someone said I wouldn't look funny as long as I put a pro lens on D40.
I probably can't use this Nikon 70-200mm f/2.8G ED-IF AF-S VR as much inside the house. This means I must get another lens for the indoor use under low light situation in additiona to this lens. I could probably still add a lens for the inside the house. I need a VR function because the hardware will be used by my wife, who always ruin a shot because she can't keep her hand steady. Please remember my subjects (dogs) are moving fast erratically and I need the ability to shoot under poor lighting inside & outside of the building. Thank you again.
You'd want to be shooting at a high enough shutter speed shooting dogs (1/200s or faster minimum) that I don't think holding something steady is going to be an issue. Blurry shot is mostly the fault of slow P&S cameras and not the photographers. Heavier pro lenses are heavy enough that they have a higher moment of inertia and in effect can stabilize themselves to some extent.
But f/2.8 is still slow for indoor low light shooting. With it completely dark out and just relying on household lighting, I can get about 1/60 to 1/125s at iso1600 and
f/1.4 with my D80 and 50mm f/1.4D prime lens. That's four times more sensitive than an f/2.8, or two stops. So at the same ISO you'd only be getting 1/15 to 1/30s shutter speeds which is barely quick enough to posed shots, let alone things that move with an f/2.8. Even if a D300 gave you acceptable results at iso3200 (one stop better) and 1/30s to 1/60s at f/2.8, that's still too slow for any sort of motion. This is why you'd need either a flash or several flashes, or a much faster lens than an f/2.8 for indoor shots trying to freeze motion. Or a D3.

You probably wouldn't want to shoot at any aperture larger (smaller f/number) than f/2.8 anyways though, because the depth of field of where you're focused at becomes so slim that it's nearly impossible to keep anything in focus at all. f/1.4 is great for posed shots where you can compose precisely or for outdoors at longer distances, but is extremely demanding at close range with moving targets and not really feasible. So you're back to a smaller aperture (higher f/number) and needing a flash. That's where the superior 1/500s flash syncing capabilities of the D40 make a huge difference.
Get a D40 with a Nikkor 17-55DX or the 24-70 f/2.8 and a good flash and you'll be set. The Sigma 50-150mm f/2.8 HSM might be a great indoor lens too. Then get a 70-200VR f/2.8 for the outdoor shots. If you really want extra reach, the 70-300VR f/4.5-5.6 is a great lens too, but might not give you the speed you need when the light fades. But you can always crank up the ISO on the D40 since it looks great, and you've got 1/500s flash syncing capability too on that camera.
The best thing about the D300 for what you're describing is the fact that it'll shoot at up to 8 frames per second with the optional battery grip, and 6 fps by itself. The D40 and middle-road cameras only do about 3 fps. As fast as dogs move, you could easily miss shots between frames at only 3 fps.
Like most things in photography, there's more than one way to do things, and a lot of it depends on your own budget, style, and personal preferences. So there's no right or wrong answer.
BTW, don't forget about Canon. The 40D is an awesome camera. Combine that with maybe a 24-105 f/4L IS lens and a flash and you'd have a great setup for both indoors and outdoors. Canon generally has snappier AF performance, but that shouldn't be a problem if you can afford pro-level Nikon lenses which are just as quick.