This situation can be little awkward for sure. You probably don't want to tell your client you need to charge more, or that you want to let her go.
I would suggest doing either one of those as soon as possible. I would recommend trying to charge more at first, then if no good comes from it, let her go.
Doing this will at least see if she is interested in paying anymore, and if not, you can simply let her go and explain why (Your Expenses don't add up for this job.)
Remember to always sound nice, and make it at least seem like you are interested in the clients feelings. In sales, you want to always serve your services to people who truly need and qualify for them, if they don't and you just sell them on it just to gain a client, you are truly doing the client a disservice.
Hopefully that was of some help. Overall, try for more or let her go. It will save a ton of time and troubles down the road.