Translation:This shop has good business.
The translation is good, but far from literal. A more literal translation should also be acceptable such as: " The business of this shop is very good."
In English, "doing good business" is a phrased awkwardly. I'd like to propose a simpler translation: "This shop is doing very well"
I'm sorry, but writing 'is a phrased awkwardly' doesn't give me as a native speaker confidence in your opinion. There is nothing wrong with 'doing good business'. I agree that your suggestion is simpler, but they probably want to explicitly include the word business in there, rather than making it explicit.
I think that translating it by - this shop is running good business - would sound more English.