How can I make this deal work?

[Donny Trana]

Here's the situation: 

I have a house for sale. A woman contacted me today and said she found the house I have for sale online. She is very interested because of the location and price point of the house. 

Her situation is that she is being transferred for her job (with the department of transportation) to the area where I have the house for sale. She needs to be here within the next 30 days for her new job. The problem is, although her employer has agreed to purchase her existing house, the closing won't happen for 60 days. She's wondering if there's a way for them to move into my house within the next 30 days. She says they have been prequalifed with a letter from Quicken Loans and that when their existing house closes, they plan on putting more than 50% down on their new house (apparently they have decent equity in their current house)

My question is.. what kind of contract or things can I do to help make this deal happen but still protect myself in case things do go wrong. She seems very honest and legitimate but obviously I'm not just going to take her word for it, heh.

Any advice would be greatly appreciated. This is the first time I've come up against a situation like this.