I am in your exact same situation! While I don't think it's the most professional thing to leave your first job before a year, you have to do what you gotta go. I have secured a position exactly like yours, I am of course thrilled, but the pay in my area is incredibly low. There is no union or anything here, so nurses in my area are really just getting screwed. With my mass amounts of loan debt, and after taxes taken out of my paycheck, I don't see myself living a comfortable lifestyle and still paying my bills here. Therefore, I am looking elsewhere for jobs, even though I've just began this job. I know it may not be the right thing to do, but it'd be silly for me to be unemployed and live off credit cards - and it's not my problem that they are underpaying us.
As far as in terms of your job search
, I think it depends on the specific location you are going to. I am still applying for New Grad positions, and things like "Staff Nurse I" positions. I have less than 6 months though; if you have six months or more, you should target your search towards hospitals/positions that use 6 months as a minimum (a lot surprisingly do). Definitely would not hurt to keep applying to New Grad jobs and see what happens.
I do think things look up a bit more when you are out of school, licensed, and are getting technical experience. It can't be harder, right?
Best of luck.