On Screen (touchscreen) Web Keyboard
Google yields lots of examples of this type of thing but nothing looks obviously better or more widely accepted than anything else. Am looking for someone with firsthand experience or a definitive link to something up and running and being used effectively somewhere.
I would recommend you look outside the web site / HTML / JS context. I imagine a lot of problems with this approach, especially the fact that you would have to work with a frameset to get it displayed persistently. Apart from people not seeing the real URL in the browser bar that way, it can be too easily busted out of, either manually or though a frame buster script.
As I said in the comment, Windows XP tablet, (I think) Vista and (I know) 7 bring decent, dockable, built-in keyboards. An IPad does, as well, obviously.
There's also a Firefox extension designed to provide a keyboard in Kiosk mode.
Maybe this could help: Creating a keyboard with css and jquery