As far as i understood it the whole system is browser based. So you can enter it from every browser enabled device.
edit:
lost of thought here, lol.
i guess there will be an app for 3ds but it will be browser based. Just like the wii shop channel.
I think there will be some built-in 3DS implementation -- maybe akin to a browser, but hopefully more integrated with the system than that.
Nevertheless, we do know that Miiverse is planned for "any web-enabled mobile device" so clearly there is at least some browser implementation going on here. It sure looked more like an iOS app in that skit though. Maybe they will have that too? I dunno.