Got as used in your example is very commonly used in AmE, it has the meaning do you have
A very famous ad campaign by the US dairy industry used the tag line
Sure do means of course we do or you can bet we do, its feeling is a bit more playful and informal than a business like yes we do
The combination of got and sure do would possibly place this conversation in the Midwest region of the US.
Got also has the meaning of understand
P1: Did you get what he said?
P2: Yeah, I got it.
means yes I understood what he said. This meaning is in common usage today and was used extensively by the est movement in the 1970's.
All these examples are very colloquial and common plain speak.