Once you've loaded up the books on the new Kindle, go to to "Archived items". The first option will be to import collections from another device on your account. Be sure wireless is turned on and click it.
Of course, if you've already de-registered the old Kindle -- so there is no other device on the account -- this won't work. I don't know whether the information will come back if you re-register the old Kindle, assuming you still have it. I do know that when I de-registered my K1, gave it to my son for a few months, and then got it back and re-registered it, Amazon knew the name I'd given it and not the one my son had registered it as.