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It sounds like you have already thought this through, weighed the pros and cons, and know the answer, but you’re just looking for someone to give you permission. 
 

Yes, being in a job, much less your first job, for under a year is not the best look. Yes, you will be (accurately) viewed as someone without any experience and will probably be lumped in with people straight out of college. None of this is ideal. 
 

But man, life is too short to be in a city you hate working a job you hate. I’d start looking today. Tell a logical, honest story about why you want to work in a different city and in a different role and pound the pavement. With the current job market, your less than ideal situation, and you trying to make a career and location change all at once, you may end up being in your current role longer than a year anyhow. 
 

You don’t need permission to do what’s best for you. No one out there can give it to you. Move forward. Make things happen.