Oh, I am sorry you are going through this. It is really discouraging as you are transitioning the child, getting to know and enjoy them and then poof everything changes in an instant. Unfortunately that is the nature of this business.
The Mom did give you ample notice of her child's departure. Perhaps you could have accepted the notice and proceeded with care until the child's last day as you don't have a replacement.
I have been blindsided a couple of times to and have learned not to react until I have given the situation some thought. In my younger days I was very much a reactionary and found it never helped a situation. So now I control the instinct to react strongly.....nothing good ever comes out of it.
That said, why not give yourself some time to find another family. In my area there are a lot of providers as well and it is daunting sometimes to find a new client. I have been wanting to raise my rates as I haven't for the last 3 years, but fear those couple of extra dollars a day might be enough to send a client looking elsewhere even though I run a great daycare.
Remember, a lot of people do not want to put their child in centre care for many reasons. They prefer the more personal touch of a home daycare and like not having to pay centre prices.

You can also keep an eye out for a home based business, but you will probably be dealing with different clients who will disappoint you in other ways.

Keep your chin up and carry on. I am sure you will find another client. Just let the shock of this departure wear off.