IDNA has been a standard for 20 years. You can already do this.

However, they are IRI, not URI, and IRI support is sparse because of its dubious broader value.

“Dubious broader value” is a great way to tell you’re United-Statesian without saying you’re United-Statesian.

Note that the second link is a table of Internationalized ccTLDs and .jp is not yet on it. So you can't do it yet.

That table shows whether the ccTLD itself has an IDN form e.g. 宝石の十字架.日本. You can register 宝石の十字架.jp just fine (obviously, if you think about how IDNA works).