QR codes aren't contained in some exotic filetype; it's just Unicode text. They do usually contain a link, in practice; but the OP is saying that they should just encode a plaintext version of whatever is on the destination website, and also contain a link that the mourner can visit if they wish for images or interactive content.
Indeed, you can fit about 4,200 alphanumeric English characters (so, call it about 900 words) in the biggest QR code; long enough to fit more than just an obituary, and definitely more than you'd be able to chisel onto a headstone directly; though not long enough to fit an entire life story.
Though those are also the most fiddly to print and the most likely to be damaged beyond the built-in error correction's ability to repair; to use the best error correction, you get about half that. And at version 3 or 4, which is the size you see most often, you only get at most about 100 characters. Which is why they're usually just links.