I think it really comes down to how comfortable you feel in your current skill level. That happens a different times for everyone. Plus I've seen programs require no RN experience and others that want a minimum of 2 years + so I think it really just depends on a combination of things...
One of the many things to think about would be your focus with this graduate degree. If you are thinking of acquiring a graduate degree focusing on an advanced nursing practice (APRN) such as nurse practitioner, clinical nurse specialist, midwife, or nurse anesthetist, I believe that you should be at least proficient in your role as a registered nurse --- as these concentrations will require mastery of nursing skills, advanced concepts, and advanced direct patient care.
If an advanced practice nursing role is what you envision yourself pursuing, perhaps shadowing an advanced practice nurse would be helpful in making your decision. Before pursing graduate school, I worked closely with a clinical nurse specialist (CNS) who inspired me to return to school and acquire my graduate education. Through initially, I wanted to become a CNS, I was lucky enough to be in a program that allowed dual role graduate degrees (Nurse Practitioner and Clinical Nurse Specialist dual specialization). While I initially wanted to become a CNS, I end up loving the nurse practitioner (NP) role more --- hence, why I currently practice as an NP. Every individual will have their own journey and the amount of nursing experience an individual has may or may not not have an effect on how successful they are in their graduate program. I would say however, that I felt much more prepared starting my graduate program with having 3 years of solid nursing experience under my belt as compared to if I started my program with just a year of experience.
Best of luck with your academic endeavors and looking forward to updates on your journey!