I'd call that reasonably anonymous. Pay attention to the TLD, because it might be against ToS to register some of them anonymously (mostly ccTLDs). There's plenty that don't have such restrictions.
Have a backup plan ready for when you get taken down.
I like njalla. Would be nice to see some others taking their approach. Anyone know of others that embrace the idea that one should be able to register a domain name anonymously?
Domains can be bought on njal.la, NameCheap, EasyDNS and many others.
Hosting can be bought on Simafri, Accu, and many many others.
Make sure you use Tor and VPN and NoScript throughout.
It's true that you need a hosting provider in addition to a domain name. It's good to discuss privacy-enhancing domain name registrars and privacy-enhancing VPS providers in the same breath.