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:
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....