But a small remote won't do because there isn't one that will work with the iPad.

Yes, AppleTV has Bluetooth and as far as I know, it should work with the iPad - that's the primary device one would AIrplay with, not counting Airplay enabled audio systems and speakers which are audio-only.

I'm trying to find a demo to look at, but I haven't found one yet. I'll probably pick up an AppleTV but I was hoping Apple would bump the specs on a new version before I pulled the trigger. I'd like 1080p output.