A good $1,000 DSLR for shooting low light video?

[Ferdyvideo]

As has been said before, you're probably better off investing in a faster lens. A 50mm 1.8D lens would be a great place to start. You'll be surprised how much this will increase the image quality of your footage.

Also as a little side note, you might want to take a look at noise reduction software. Neat video is probably the best one out there. This little piece of software really helped to improve my low light footage in post-production.