You might need to ask YOUR attorney about this one, but in my opinion; a deposit is not rent. If she left the property in average to good condition she should have her deposit back, that is what this money was for. Depending on what type of lease and what document you used, the language of that document will pretty much tells you what remedies you will have if the tenant breaches her lease. That is why, my first line suggest you look for legal advise, as a Professional Realtor I think that is my best advise.

Now, I am also a landlord, reading your question, I can see that you did not really lose much, one tenant left and in 4 days another moved in, I would simply give her the deposit and go on with life. It will cost you too much money to try and keep that deposit and the first time you need to talk to an attorney it will cost you even more. I don't see you wining this one. Be glad you did not have your rental vacant for long.