An unlicensed driver totalled my car. Can I sue her?

I recently let a coworker borrow my car. She asked if she could drive it and I didn't see a problem with it. She did not inform me that she didn't have a license. She ended up having a wreck and totalled my car that I had bought less than a month ago. My insurance covered the damages to the other car but as I only had liability coverage it didn't pay for the damages to mine. This has put me in a financial hole and she is refusing to reimburse me. If I took her to court, would it hold up?