In this hot rental market, I would tell the potential tenant that if it is still available on April 1 she/he can apply. The person probably has to give 30 days notice and does not want to pay double rent for a month, but doesn't mind that you will be out the income for a month.
I have split the time in a slower market. In that case their lease is signed and deposit & rent paid immediately.
Have you done a background check and credit report yet?
Historically since I've had my places this is a terrible time to have a vacancy. It's slow for people to move and the quality of tenants are poor as they are usually getting the boot from somewhere else. Back in October I advertised a 1 BR and had so many responses I had to stop showing the place. This 1 BR I've had only 4 and this girl that doesn't want it till April 1st because she currently is in a lease till 3/31 is the best that has looked at it. So in a small town it's somewhat different than in bigger areas. But I agree with some type of holding fee and an agreement binding her to signing a lease or lose the fee. We'll see how it goes. Thanks for all the advice.
Yes--the solution is either to split time (tenant pays half of March) or move on and find a different tenant. Do not even consider this option, however, unless the tenant has good credit and is otherwise qualified.