Is 做事 just Taiwanese, or does it have a different flavour than 工作？
I think you are right - "做事" is probably only used in some areas of China, especially some southern areas where ancient Chinese has an influence, and not as commonly as "工作" in this sense. I would say it is more colloquial than the latter, too - for example, I think an interviewer will more likely to ask "你之前在哪里工作？" than "你之前在哪里做事？"