Training a puppy is a LOT of work, and with your daughter being only 9 months old, this may not be the time to take on that kind of commitment. Also, puppies are just beginning to learn that playing with people is different than playing with other puppies. Many people opt for getting an older dog when there are children involved. Older dogs are usually more mellow. There are wonderful dogs available for adoption at the humane society, you may want to start there.
Most shelters do an excellent job of behavior profiling and know which dogs are good with kids.
And these aren't just mixed breeds. A number of purebred, pedigreed dogs can be found at your local shelter. It is difficult to fathom all the reasons pets being relinquished. Get several opinions. Talk to your local veterinarian where you would consider taking your new dog.