If you want a purebred dog, try a purebred dog rescue group (like Poodle Rescue, Boxer Rescue, etc). Even though you are wanting to do this ASAP, most groups have an adoption approval process to make sure the dogs are going to a good home. On the other hand, the dogs have been fostered in homes, and for the most part temperaments are known, how they deal with children/other pets, they are spayed/neutered, up to date on vaccinations/HW prevention and have been treated for heartworms if HW positive.
I worked once with Boxer Rescue and Lab Rescue and there are some really great dogs that come through these groups, and I'm sure that holds true for other breeds as well.
As a veterinary nurse, I recommend that young adult dogs are better for children than puppies - it's a safety issue. Some older dogs have lived with children their whole lives and love them and would be a great starting dog for your daughter. You know what works best for your family, and Rescue groups work with individuals/families to place dogs with the best family so that rehoming will hopefully never be an issue again for that dog.
I will also say that, although I have had mixed breed dogs and have nothing against them, if you want a purebred dog, you can get a better idea of temperament and health issues for that breed. Personally, I chose now to have purebred dogs for that very reason and go to reputable breeders to buy my dogs.
Remember that obedience class for any new pet is always of great value! It helps establish the relationship between you and the pet, making the pet feel safer knowing its boundaries.
Good luck finding the right dog for your family.