Apple has released an updated to its free, universal Remote app for iPhone, iPod touch and iPad alongside iTunes 11. This update, version 3.0, adds "support for iOS 6." It's also got an updated icon, replacing the black "play button" in the center with a grey one.
I played with it briefly this afternoon and didn't notice too many immediate changes in it's look or behavior (and I use it often enough to notice). The Up Next feature now in iTunes 11 is supported, so you can see and edit upcoming songs. Search is also improved, showing results as you type. Grab it now and enjoy the increased support!