If I deregister my kindle then reregister will I lose all my books?

Not if you sync your iDevice wih itunes. Just connect your iPad/iPhone to iTunes. Then Open iTunes>iDevice>Apps>Scroll Down to App Sharing>Select Kindle>Copy your books to any folder by right clicking and click copy then go to designated folder and paste

Its even easier than that. If you are using the same amazon account - and unless you have gone out of your way to delete the books from the Amazon server (don't ever do that) -

when you re-register, all the books will be there. You can re download any that you want to read again, or just leave them there for the future.

Probably. Why the question?