You can get it always selectable when you use the "show in menubar" in system preferences. You'll see a country flag in your menu bar, and can change the language or input method anytime you want to - so picking the character palette is one click away.
As it's not an application, it can't really be docked though.
There is not a way to do so if you are having the same problem that I was. I took it to the Bar at the local store to have the problem remedied. The tech said the fix is on the Apple site, but I have not been able to find it. But the fix for our problem is out there..... you may just want to bring it in or call. Sorry I could not give you the exact info you are looking for, but there is hope.