Does .グーグル (.xn--qcka1pmc) exist?
Yes. .グーグル (.xn--qcka1pmc) is a real top-level domain, live in the IANA root zone right now.
See the .グーグル (.xn--qcka1pmc) page for what kind of TLD it is. Note that existing in the root doesn’t always mean anyone can register one — some TLDs are brand-restricted.
Try to register a .グーグル (.xn--qcka1pmc) domain
This answer is generated from the live IANA root zone list, not from vibes. If the DNS changes, this page changes.