I would probably wait. But it depends on you and your family. When my dog passed, I simply couldn't get a new dog for over a year. I tried to push myself to do it and tried a few rescues on a trial basis and the grief was just too strong still. It was only until I had worked through my grief that I could welcome another dog into my home. I know other families, however, that find it best to get a new dog right away- sometimes the day after the last dog passed away. I don't think it would work for me, but it does work for them. I did try it once, when I was a teenager, my ferret had passed away after a long battle with cancer. I was devastated, and my parents pushed me to get a new one with a week or two of his death- I of course, looked around, didn't find anything, until I saw this one little guy who was obviously sick, too young to be legally sold, and bite wounds from his cage mates. Needless to say, he wasn't staying there and came home with me. I have vivid memories of holding the little guy and just crying because he wasn't the ferret I had lost and never could be. Not quite the way I'd want to invite a new pet into my home.
Anyway, grief issues aside, I think you should think about timing as well. If you get the dog now, depending on breed, by the time your kids are school age and can really play with the dog, it will already be approaching old age. And thats just your oldest kid. Small dogs do tend to live longer, but they still tend to slow down with age. Say you get it now, by the time your first is 8, the dog will be 8, if you have another child 2 years apart, by the time that child is 8, the dog will be 10. Not that I don't think old dogs can be great pets, but if the main objective is to have a dog for the kids to grow up with, I'd get it a little later, so they can remember watching him grow up and will be able to roughhouse during his younger years, and will grow older and more sedentary as they approach their teen years when they are likely to have less time for the dog.
There's also something to be said for dogs raised with children- if you get the dog before the baby, it will settle in, and then you may have to readjust once the baby arrives. If you wait till you have kids, the expectations for the dog will be there upfront- you wont have to deal with a dog that wasnt socialized with kids, because the kids were there from the start.
Finally, what can YOU handle? I assume you would be the primary caregiver? I cant imagine having say, an adolescent dog and a 2 year old. that just sounds like a lot of unnecessary stress. Plus kids that young and dog must ALWAYS be supervised together, do you really want to be juggling a 2 legged toddler and a furry toddler at once? And with a baby in the house, will you have time or energy to properly train and social a puppy? If you don't maybe waiting until the kids are a little older would be a good idea.
Those are the thoughts that come to my mind, I'm sure other people have different perspective. My condolences on the loss of your dog, its tough to lose a pet.