Hi there - just posted but my answer didn't seem to take - so I'll try again, excuse if a duplicate.
It sounds to me as though you have established a good payment record with your current landlord, that will go along way. Be prepared to provide an explanation if your credit score is suboptimal, and provide verification of consistent and timely payment to current landlord. Add to that employment verification and some recommendations and you should be off to a good start.
Good luck to you,
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