Are all bluetooth keyboards slow to respond?
No! What you have been told is simply not true!

I have been using Apple Wireless keyboards for 8 or 9 years and have not experienced these problems. Neither have I experienced similar problems with a Magic Mouse or Magic Trackpad.

That said, without further troubleshooting it's impossible to say why you're having these problems. It could well be that the issue has nothing to do with your keyboard and something else is at play here, but the simplest way to rule that out is to try another wireless keyboard and see what happens.