Hi C.,
Yay for your little one who is ready to move! It's a whole new challenge once they are mobile. I have a 22 month old son and a 2 month old daughter. I read the other responses and agree with what many other mommies have said about creating a safe place for your son to be where he can move and play while you ge things done. My son never liked playing in his pack n play, so we ended up getting a super play yard. It's a gate that forms an enclosed area. I would put toys in there and he would spend some time in there playing on his own so that I could do other things. Of course, I would keep this area nearby and in view, but it gave me some freedom to cook, do laundry, etc.
As for the dogs, I think that most important thing is that you always monitor their interactions. Know your dogs and what they will tolerate, and what you can expect from them. At this age, it is much easier to keep them seperated than it will be down the road. I had two dogs until my son was about 17 months old. One of them had a history of anxiety induced aggression. We were working with him on obedience, took him to a behavioralist, and he was even on medication. I was diligent about keeping him away from my son, or being right there if we had my son on the floor. Unfortunately it was, for me, impossible to keep them apart and/or to be right there ALL the time once my son was really walking and climbing, etc., and was not confined. This dog ended up biting my son on the hand and we decided that he be removed from our home. We found a rescue and hope he is happy. I was pregnant again when this happened and could not responsibly keep this dog.
Our other dog has been fine with him, and we allow them to be together all the time, but we are always watching to be sure that my sone does not hurt the dog or antagonize him. When the dog does not like what my son is doing, he walks away. I am also trying to help my son learn to interact with him appropriately. I am confident that this dog will not hurt him, but still watch their interactions closely, just in case my son pushes him too far or hurts him.
If your dogs are generally well-behaved and do not have aggression issues, I am sure you will be fine as long as you monitor their interations and try to anticiapte any problems. I found it very difficult, once my son was walking, to keep him away from the dogs. He became more interested in them and, being more mobile, would go them and follow them, etc. So, for me, sepeating them was not an effective long term solution. They needed to learn about each other under our supervision.
Good Luck!