There are other good reasons to register your copyrighted design before and not after it's been infringed. You can't sue for compensation for profits that were made before your copyright was registered. You can only get compensated for profits that were made after registration. Without registration, your copyright protection enables you to send a cease and desist notice to get that person to stop copying your work.
That's how I understand it anyway. Consult a legal expert for actual advice.