Copyright is an automatic right. Everyone have exclusive rights to copy their own work as soon as they create it. In the very early days of copyright laws there were some registration requirements but this quickly fell out of favor as it was impossible to manage. The copyright notices you see with the name of the copyright holder and the date is a practice from this time but is now just included as a courtesy.
The other types of intellectual property rights, patents and trademarks, do still have application and registration requirements. This is handled by the patent office. So you should look to them for registering your intellectual property and possibly contact a lawyer specializing in this.
Copyright starts automatically as soon as your idea comes into existence.
That said, there is the burden of proof. You need to be able to prove that you were the first with the idea. Sending it to yourself as an e-Mail is a simple option, because it will be timestamped. Just have to hope that the e-mail provider doesn’t shut down until you need the proof. Sending a sealed letter to yourself and keeping it sealed should also work, because the post will put a stamp with a date on it.
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