I think I would be more positive if you had said "my wife/I can't stand living without a dog" or "I know a puppy is almost as demanding as a human child, but my home is empty without a dog". I don't think wanting to have your child grow up with a puppy is a wise basis for choosing to add another living creature to your home at this point in your child's development.
Honestly, based on my personal experience, I don't think a puppy is a great idea until your child is age 3 and then is risky unless you and your spouse are willing to put a LOT of time into the puppy's education. I think it really depends an awful lot on many factors:
1) the temperament of your child, is she gentle, is she obedient, is she calm?
2) How much time are you and your wife willing to devote to training your dog? If you are not BOTH 110% on board with obedience training and supervising your child and puppy at all times then you are a disaster waiting to happen. If you both work full time, your free time is taken up with your human child and your puppy doesn't get the time and attention he needs. The puppy needs to receive enough education and attention to reach his full potential.
3) Do you have a toy room that is separate from your main living area? Children's toys and puppies do not mix. An unsupervised puppy will eat an entire barbie doll in 10 minutes and it will cost you a few thousand dollars at the emergency vet, if it doesn't kill your dog. (I speak from experience on this)
4) I assume since you're posting here, you're interested in goldens... are you familiar with the energy level and amount of mental and physical excersise they require on a daily basis? They are going to be be more demanding than your previous pet. I was constantly amazed by my golden's desire to retrieve and need for a job... he was not just a couch potato for many years.
My first golden came home when my daughter was 2 1/2 years old. My daughter was an extremely unusual toddler - calm, obedient, very verbal, empathetic of others feelings. I was a stay at home mom and was able to spend a lot of time on obedience. Even though it went well, after that, I always said I would never bring a puppy home with a child in the house younger than age 3, ever.
My youngest is 3 1/2 now and our new puppy will be coming home at the beginning of the new year. I am looking around my house and realizing we have a lot of picking up to do around here to puppy-proof and make it safe.
I hope you will visit breeders in your area and spend time with them to make sure you really understand the committment you are making for your family if you add a puppy in now. A 60 or 70 pound, excitable golden is a bull in a china shop when un-restrained around children, and most goldens under the age of 3 are ALWAYS full of zest... they knock children over from love, not malice but it will still makes your child cry.
An older dog adoption might really be the way to go.....