This has actually been done:

https://esolangs.org/wiki/Hello

While quines (programs that print their own source code) aren't possible in Hello, there's a version that makes it possible:

https://esolangs.org/wiki/Hello_Plus_Plus

And if you say the original isn't good enough because it can't do anything else... well, esolangs have you covered there too:

https://esolangs.org/wiki/HQ9_Plus

(It should be noted that these are all joke esolangs. There are actual languages on the wiki that are very interesting though - I would definitely recommend you take them out!)