I think this is an excellent idea! It's a little cost effective since most dogs are spayed/neutered and up to date on vaccinations. When I fist got Kaji (at 12 months old) he was $500, and I immediately had another $400-$500 in vet fees. (wellness check, heart worm meds, flea preventative, neuter with pre-op blood work)
I think rescues and shelters are a great way to add another family member. Your daughter will never forget this lesson and will have her own buddy to spend her afternoons with. I hope you're prepared to bond with the pup too. It seems pups tend to bond with the adults since we're the ones that look after them the most. Either way, everyone can enjoy the new addition.