Are you restricted to any sort of strict budget? If not, go for a 300mm f/2.8, a D3s and an SB-900
, I'm assuming that you're restricted and can't afford gear like that which will cost you upwards of $15,000. I think that three options could help you.
Regarding upgrading to a D7000, you won't see a huge difference. The D7000 will be better for sure, you'll be able to go up to ISO 25 600 in a pinch (hopefully you won't need that, though!), and it's generally a bit cleaner. If it's too noisy, you'll also be able to reduce it to almost nothing with NR software such as, my personal favorite, Noise Ninja. The extra resolution doesn't help too much, but if you make huge prints it may be nice to have. What will make the biggest differences would be the faster 6 FPS shooting to capture the action, plus the external controls to quickly change settings. Those features will make sure that you're there to get the shot and you're given the opportunity. Of course, that doesn't mean that your photos will be any better if you don't know what you're doing!
Your next option would be to purchase an external speedlight flash. An SB-600, SB-700 or SB-800 would probably fit you nicely, you'll then be able to bounce light and have more control over the lighting of your subject. I don't regret purchasing my flash, it's great in low light. However, you'll have to make sure that you'll be allowed to use the flash near the dogs. I've done some obedience in the past as well, I do have three dogs
of my own, and I don't think that they'd react too badly to a flash, but that's my dogs.
Your third and probably best option would be to purchase a faster lens. An f/2.8 zoom would be great, however they're very expensive. The Nikon offering is $2200 new, but second hand versions of previous generations can be snagged for as little as $800 or $900. New versions from off brands such as Sigma or Tamron run <$1000, so that may be a better investment. You'll lose 100mm at the telephoto end, so if you need the 300mm it may not be a good idea, but otherwise 70-200 f/2.8 zooms are excellent lenses for telephoto use. If you need the 300mm, consider a 300mm f/4 AF-S.