In order to answer, it's worthwhile looking at the differences between field, occupation and career.
What is your field of working?
A field is a particular branch of study or sphere of activity or interest. Field is often used to indicate a specific occupational area or academic branch (e.g.civil engineering, physics, marine science), rather than referring to a specific job. In other words, it's a person's area of expertise, and it's common to ask the question in such a manner:
- What is your field of expertise?
A person does not have to be currently working (or working in that occupation) in order to have a field.
What is your occupation?
occupation refers to the field or type of work you perform. For example:
A: What's your occupation/profession?"
B: "I'm an accountant." or "I'm an engineer."
Profession is another term worth mentioning here. Occupation and profession are similar in that they both refer to the general type of work a person does (or would want to do). The difference is that an occupation may require specialised training, such as an apprenticeship, while a profession normally requires some form of third level education in that particular field.
What is your career?
A career is the total progression of a person's professional life, and can include many different jobs over the years. For example, if a person had a career in politics, it means they could have many different jobs over many years, all under the broad umbrella that is 'politics'. The being said, it's not particularly common to ask a person 'What is your career?'
Given the answers you've provided ("Accountancy", "Nursing", "Medicine", "Engineering"), these are all fields of expertise, therefore it would be acceptable to ask:
A: What is your field of expertise?
B: Engineering is my field.
IF you wanted to ask about occupation however, the answers would have to change somewhat:
A: What is your occupation?
B: I'm an accountant/nurse/doctor/engineer.