New grad RN accepted job and wants to continue applying for other jobs

I am a new graduate RN and have just accepted/started a new job at a local hospital. I did not particularly want this job but thought it was my only option to get experience since the position did not require any previous experience. I have recently found out about a nurse residency program at a hospital in a city where I would love to live. Is it inappropriate to continue job hunting and apply for this once I've already accepted a position at a different hospital?
You can apply and see how it goes. However it will not look good that you are trying to abandon another hospital so soon. It would be different if you were in a clinic or home care as some recruiters may understand new grads trying to get hospital experience however if you already had a hospital that hired you and is giving you experience and you are trying to leave them they may fear you would do the same to them once an even better hospital may come along. I would say stay at least a year in your current hospital so you not only get experience but also show you were able to stick with one hospital employer for a year.