We already had our rescue dog when DS came along - so I would say that its perfectly OK to cope with a dog and a baby - and you can bring them up so that they know how to behave around dogs - our dog knew that we would stop DS from doing anything bad to her.
I loved having her when DS was little so that we went out for walks with the buggy - she adapted very well. Its also a really good excuse for getting children out for a walk - the dog needs a walk so that they have to go out, whatever the weather (and, believe me, we've walked in everything that England has to offer in terms of weather and resultant ground conditions).
But you've also got to be prepared for your children to teethe on the dogs toys (I did take it away from DS as soon as I saw, honest ) and put on more washes as you deal with the muddy clothes as they fall over trying to keep up with the dogs, or get involved in a muddy football session with them.
I don't have kids but a lot of my friends do so I know roughly how it works Based on that you might want to ignore my advice, but having taken on two rescues in the last year (one at three, one puppy) I would probably want to wait until the little one was old enough to understand the rules on how to behave around a dog. Otherwise supervising them adequately could be very stressful.
Personally i wouldn't while your kids are so small. Dogs take up a lot of time - especially if you choose a puppy. Maybe an older rescue dog would be good but many places won't place them with children.
We have a 3yo dd and a 6mo ds. I am on mat leave, but would normally work a 3 day week. Of those days, dh is here one day and my mum the other. My brother lives here too and loves dogs. Is it mad to think about getting a dog (or even 2, to keep each other company) in this situation, or would you do it? Our last dog died a few years ago and we did say we wouldn't get another, as it was heartbreaking, but I have changed my mind!