Just to add my two cents here as a native Memphian:
Your home is in a fairly nice area. Newer area than my own neighborhood, and fairly close to the world headquarters of FedEx, a major employer in Memphis. But looking on Zillow, it's easy to tell there are a number of homes for rent in the general area for similar pricing with yours. As others have mentioned, this time of year is not the best for people moving, and there should be more activity in the spring and summer.
What comes to my mind is the old cliché: good, fast, cheap, pick any two. You have three factors, rental price, tenant quality, and time on market, and you can pick two. I.e. if you want good renters to move in quickly, you will have to make the price cheap.
Your rental price seems quite reasonable for the area, but having a fair price doesn't change the fact that there are lots of rental options on the market and not so many people looking to move in the middle of winter.
Real estate is not a microwave way to make money, it's a crocpot method, and if your house sitting empty a month or two is causing you this much stress, then you might be better off investing in something else.
I know it must be frustrating to have it sit empty, but I hope you don't think real estate investing is all a hoax just because you are experiencing this issue with vacancy up front. It is intoxicating the first time you get a rent check, or at least the first time you have a month with no issues and still get a rent check. At least it was for me. Seems too good to be true having someone drop off money and I didn't have to do anything. Amazing, lol.
But as you are finding out, there are issues to be handled, it doesn't all go your way, and so it's not for everyone. There's a reason most folks are happy with their mutual funds.