The DSi has pretty weak hardware. It may be possible, but it would not be pretty, nor something desirable.
Besides, it would be very locked down..., friend code only...., about as useless as WiiSpeak Channel.
I agree, I expected video chat to come very soon after the DSi was launched. The video could be very low quality/resolution, so streaming it between two DSi devices should not be an issue. DS Wireless communications are already in place to send info between two DS systems, so everything is there that allows video chat to exist. Nintendo just needs to realize that people want it.
It doesn't have to be Nintendo. Skype could easily implement their own product, much like they have with the PSP and iPhone. And if it is Skype who finally implements the software, the communications don't have to be just with other DSi-s.