Welcome to YT.
I'm sure you'll find a pup that is the perfect fit for your family in time. Have you thought about going to a breeder? The new pup may have to be altered, but maybe not your current one (although I'd hope good breeders insist that all pups in the house are spayed - the same as rescues).
This is done because there are millions of dog euthanzied every year for lack of homes. They just don't want their pup to end up in a family that will breed it or continue to breed their current dogs and contribute to the overpopulation problem. Perhaps they would make an exception if you explained why you aren't spaying your girl now? They are all looking for owners that will make very good medical decisions for their adopted pup and spay/neuter are generally considered the healthiest route. Good luck in your search.