In standard English, I think "don't got" has the same register as "ain't". It's definitely not correct, but very common. Avoid it in any high register situations where standard English is used, e.g. an interview, a presentation, a company report.
I sometimes will say "ain't", e.g. "that ain't worth it" in informal contexts but I don't think I would ever say "don't got".
Using done for did is definitely a hallmark of uneducated dialects of English, notably but not limited to rural Southern and Western American. But I have never heard anyone use that as "Done you do it today?" or "Done you it today?"
Nevertheless, there are some rather twisted and arcane constructions on record using done. Take for example the "crows" scene from Disney's 1941 movie Dumbo, a rather racist (cf. Jim Crow, a pejorative term for Negro) depiction of African-American dialect (which would have been an extension of the Southern American dialect). One of the lines in the song the crows sing (about 3:45 in the clip) is
Well I be done seen about everything
When I see an elephant fly.
That said, this depiction is also meant to represent uneducated speech.
You will sometimes hear this doubled up with did for emphasis: