Can we be GDPR and ISO 27001 compliant with 1 employee?

ISO 27001 was designed to be applicable to organizations of any size and industry, so it is possible to be compliant with this standard with only one employee, as well as when working with freelancers/consultants.
 
GDPR refers to the process of personal data by organizations/professionals so it is not referred to dimensions, since it is applicable also to professionals, sole traders, and freelancers. The implementation depends on the kind of data processed.

These articles will provide you a further explanation about ISO 27001 and GDPR:

• What is ISO 27001 https://advisera.com/27001academy/what-is-iso-27001/
• Where to start from with ISO 27001 https://advisera.com/27001academy/knowledgebase/iso-27001-where-to-start-most-important-materials/
• 9 steps for implementing GDPR https://advisera.com/articles/9-steps-for-implementing-gdpr/
• Is the GDPR applicable to our company? https://advisera.com/eugdpracademy/knowledgebase/who-needs-to-be-gdpr-compliant-an-easy-explanation/

These materials will also help you regarding ISO 27001 and GDPR:

• Book Secure & Simple: A Small-Business Guide to Implementing ISO 27001 On Your Own https://advisera.com/books/secure-and-simple-a-small-business-guide-to-implementing-iso-27001-on-your-own/
• Free online training ISO 27001 Foundations Course https://advisera.com/training/iso-27001-foundations-course/
• List of mandatory documents required by EU GDPR https://advisera.com/articles/list-of-mandatory-documents-required-by-eu-gdpr/
• EU GDPR Foundations course: https://advisera.com/training/eu-gdpr-foundations-course//