For many questions in Chinese, it's best to respond by repeating the verb. Here's a few I just made up:
Q: 你是哪儿国人? A: 我是中国人。
Q: 刘老师找什么? A: 刘老师找她的老公。
Q: 她有老公吗? A: 对,她有老公。Q: 小王怕什么? A: 小王怕狗。
And I can think of many others (你想吃什么? 你在看什么?你在学什么?你的牙疼吗?). But this one breaks the rules:
Q: 你做什么工作?
A: 我是医生
Or we might respond 我是老师 or 我是校长, or 我是职员, etc., depending on our job.
Question: Is there a way to respond to 你做什么工作? starting with 我做...?
Perhaps there's something inherently wrong with answering the question starting with 我做....