I recently used the D7000 to shoot a documentary for a school class, and overall it worked quite well. However, there are a few things to take into consideration.
You can film with nice quality on the D7000 but only in Manual focus, Auto focus really really sucks.
I also wouldn't recommend using AF, it's noisy and slow. If you want usable real-time AF while shooting, the Sony Alpha models that use the translucent mirror work well.
Any movement of the camera i.e. running to chase a subject or just handheld, it can just look like your good mobile phone footage - gets very pixelated.
Things improve a LOT when you use VR, otherwise be prepared to apply quite a bit of shake correction filters in Premiere, Final Cut, etc.
Also keep in mind that while the D7000 does shoot in full 1080p HD, you're limited to 24 FPS. All newer models offer 30 FPS at 1080, but the D7000 only offers 30 FPS at 720 and below. Also, 30 FPS is the fastest you'll get, unfortunately there are no options for 60 FPS or 120 FPS, even at lower resolutions.
You may want to take a look at Canons, while Nikon's definitely caught up or even surpassed them quality wise over the years (even though Nikon was first to the DSLR video market with the D90 in 2008), Canon models generally offer more manual controls, and you have more opportunities to adjust your video to make it just-so. For instance, you can't adjust the aperture on Nikon cameras while filming/in Live View (unless you use a lens with a dedicated aperture ring), nor do you have many options for audio input or audio control.
All in all though, you'll get excellent results any way you go. Obviously you'll get the best of the best with the D800 or 5D III, but you'll also be spending upwards of $3000. The D600 or the 6D could be great choices, they're full frame bodies that won't break the bank, but ultimately the decision is up to you and you won't be disappointed with whatever you choose.