That will depend on the landlord. If you are willing to give double deposit, have a good rental history and stable employment, you are likely able to find a home for rent. You may want to ask for a reference letter from your current landlord that you've been a good tenant and have been paying on time.
I hope this helps! Please give me a thumbs up or choose best answer if this helps you.
Susie Kay, Realtor
Certified Home Stager & Senior Real Estate Specialist
United Real Estate Dallas