Investors instead take low-paying deposits and place them into short-term treasuries.

Rent Roll showing current rent rate, deposit, lease term, concessions, unit type & arrearage.

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

They do however need to be leased out and you will have to show the first 2 months (or 1 month and security deposit) being paid to you from the tenant on each property. 

I have 1.5 months of security deposit.

She has offered to pay 3 of the 5 months  but keep her deposit and last months rent.If we let her go, having some buffer to find a new tenant would be nice but the fact that we need to find one during the holidays and leading into winter does not sit well with me.

Another option is this: what you can do is take a deposit to hold the place (and have a signed deposit to hold agreement), but they forfeit the deposit if they fail to rent.

@Brandon Carlson no deposit? 

Maybe they really want to move into a SFH and they need a larger deposit to do so, you could trade some cash for those keys in that manner....You also mentioned that the rent was below market, if they are on a month to month lease, then you should be able to start systematically raising rent to bring them up to market. 

I uploaded a pet addendum to apartments.com, asking her to fill out, along with a pet deposit.