The documentation of your boat extends nothing to the dinghy. If you register the dink where you live now you''ll also want to make sure you carrry the title with you when you travel.
The dingy registration unlike the documentation of the main vessle expires regualrly so later on when you leave where you are now you will need to renew it. If you have the title then you can renew the registration when the current registration expires. It may not be easy to renew it back where you used to live if you no longer have a decent mailing address. It may prove easier to just renew it where ever you are and always carry some valid state registration where ever you operate the dingy motor.