Hi there!
As an American English speaker, both are correct.
"Do you not" would be seen as more formal and probably a little old.
"Don't" is a contraction of "do not."
In your speech, I would recommend using "don't," because it's much more common.
So really, above, you're asking the same thing only one uses the contraction and the other does not (doesn't!).
Hope this helps!
-AmyV