If we have no one doing a job similar to that of a female employee, do we need to worry about her making a claim under the Equal Pay Act?

Yes. She does not have to restrict her comparisons to people doing work that is the same. It could be broadly similar - for example, a female cook could compare her work with that of a male chef. It could be rated as equivalent under a job evaluation scheme. Or it could be work which is different in nature, but demonstrated to be 'of equal value' - possibly by using an independent expert to assess the value of both jobs. 'Equal value' claims have succeeded where cooks compared themselves to carpenters, and speech therapists to clinical psychologists.