I have to agree with Marda. Even among breeds that are child-friendly, you'll find dogs that have food-guarding issues, etc. And a toddler isn't going to be able to remember to keep her hands out of the dog's food, water, poop, etc.
Our baby loves dogs, but she also loves elephants, and I'm not planning to get her one. :-)
If I were to get a dog when she's older, I'd get one that had "flunked out" of a guide dog training program. They are very sweet, calm, and well-behaved--only a small percentage graduate because they have to perfect a lot of skills. Be aware though, if you choose a Golden Retriever, that they are really "people dogs" and should not be left alone in the yard or an empty house. They really need to be with their people.
You can get plenty of "I never dreamed my dog would do that!" stories. My girlfriend's dog turned suddenly on their kitten, who had wandered NEAR the dog's food dish, and sank her jaws right through the kitten's skull. The kitten is fine now, but it was rough going (and costly). Their 3-year-old was traumatized by the incident, and of course it could have been her hand or arm instead.
On a happier note, you can get plenty of dog fixes in other ways! You don't have to own a dog to enjoy them!
Our 19-month-old has LOVED dogs for about a year now. We take her down to PetSmart to watch them cavort in the doggie day care--it has a big glass wall and there are usually about 25 dogs goofing around. It's like a giant aquarium full of dogs!
The Parks & Rec department on the west side (Tualatin Hills) hosts an outdoor dog party each summer, with contests, agility demonstrations, and police dog demonstrations. These kinds of events are usually scheduled at county fairs as well.
We also take her to city parks where the dogs are allowed to run, so she can watch them and maybe approach a few people about petting their dogs.
In the meantime, she visits the neighbor's dog a lot, and has some very cuddly dog stuffed animals--some that are plushy and some that are very realistic. Finnegan's has a great selection.