How to protect the intellectual property rights of plush toys?

Trademarks can't achieve your purpose. Trademarks can only prevent others from using your logo. Even if you have a trademark, others will copy your toys, which is exactly the same. As long as you don't put on your own trademark, you can't use it to scare people.

You can apply for a design patent or a utility model patent (even an invention) for your toy. The advantage of a patent is that you can use it to prevent others from making the same toy, whether they copied it from you or made it independently.