What version of iOS are you running? I'm on 4.0.1, and all I see is "http://xn--ls8h.la/
You need to enable emoji. There are several free App store apps that will do it. One is Emoji Free! By Awesomest Inc.
That's the thing. I have emoji characters enabled, and can type and see them in text messages. It's odd I can't see them in Safari. Could it have something to do with my phone being jailbroken?
You don't need an app. Just go to Settings > General > International > Keyboards and add the Emjoi keyboard.