Hmmm...so you want a free dog? I hate to sound pessimistic (or maybe I'm just realistic), but I seriously doubt you are going to find one. Heck, I'm sure we all wish we could have found one for free...lol.
My suggestion would be to take you time and not rush into buying another one right away. Save up your money and try to better prepare yourself and your family for the responsibility of owning and caring for a new dog. I hate to think of disappointing a demanding 11 yr old, but maybe involve her in the search and preparation too for the meantime.