It’s not the best look to already be outwardly planning your leave when the unit just spent quite a bit of time and money training you. However, life happens, and a good manager in a healthy work environment should not make this “career suicide” for you. How comfortable the manager will be giving you a recommendation is something personal to the manager. At the end of the day the worst they can really say is no.
When I first graduated, I was just as go-go-go as you. I really just wanted to go straight through to graduate school. But I’m glad I didn’t. I don’t know your situation but grad schools will always be there. I recommend you take some time as a nurse to really learn how to be a nurse. At the very least a year before you think next steps. I know that’s not what you want to hear, but it will make a difference. It will help affirm your decision to go to grad school, make applying (and getting in!) easier, and, whether or not it’s fair, also make you more competitive in the job market/respected in the field. Your first year as a nurse changes and challenges you in many ways.