How long?

Since a lot of job postings state that they require a year of nursing experience, I bet employers are used to getting an influx of applications from nurses who put in a year somewhere and are looking for something else. I think it's kind of the norm in some ways for new grads to "take what they can get" and then move on to something that they like better as soon as they get that experience under their belt, so I don't think an employer would find it odd at all if you applied after a year at a job.

I think you would be surprised at how many nurses have worked at several jobs, some for only a period of months. Nurses can afford to job hop, because there is always a need for experienced nurses and we can usually land a new job when we get fed up with our old one. I had a co-worker tell me a few days ago that she was talking to a nurse recruiter at a local hospital. My co-worker commented that she had only been at her current job for five and a half years and the recruiter was like, "ONLY five and a half years? That's an eternity!", I guess compared to the other applicants that she had talked to.

I wouldn't worry about it. Go ahead and apply. If they call, then you know that they don't care how long you've been at your job. If they don't call, keep applying elsewhere.

A year is good as long as you can justify it on your resume/employment application. What employers are looking for are people who are responsible and aren't going from job to job randomly with no goals. Sounds like you have a goal and you put in a year. Give 4 weeks notice if you can; employers like it when they have plenty of notice. That way you don't burn any bridges and can rely on a good reference from your now employers.