I'm probably going to be the only one to tell you to wait.
When my daughter was 2, we got a rescue dog that was kind (completely non-aggressive) but in need of training big time! It's also part of the rescue agreement, and you have to show documentation. (Our dog was about 1.5 years old - not a puppy b/c it was also suggested that we avoid them.)
Since I was at home during that period, I was Alpha Female, which didn't make me happy b/c I was the one who had to train him. So I'd have to find a babysitter to watch my daughter as I lugged the dog to and from sessions. When I arrived home, I had to remind myself that the training had to be reinforced. But when you're watching a 2 year old (and my daughter is very good, believe me) and a dog who both want attention, you have even LESS time to yourself. And even though the dog was gentle, 2 year olds often are not. So I was constantly vigilant, which can wear you out. Keep in mind that you have to train your child, too.
Also, if you don't have a yard, you'll have to walk the dog. Try walking (and leash training) a rescue with a young child by your side. It's very difficult. And grown dogs can also make messes in the home. Our dog, if left alone in the crate for more than an hour (My daughter was in preschool 2x/week back then.), would be absolutely out of control (happy) when he was released from the crate and would go nuts around the house. So we literally had to childproof for the dog - NOT the daughter!
The trainer was also a bit surprised that we had gotten a dog with such a young child b/c the situation really made it impossible for me to follow through on anything with the dog.
Needless to say, we returned him. He's with a great family, which makes me happy, and he's being trained by their 14 yo son.
So before you decide on anything, really think long and hard about this decision. The trainer told me that many rescue dogs are returned for the same reason I mentioned above.