I have a 2yo beagle who can be very hyper and loves being involved and part of the family. He had never been around babies. We weren't sure how he would react - we knew he wouldn't be nasty etc but he is a very muscley dog and sometimes doesn't know his own strength. So in preparation for DD's arrival we bought a pet gate so we could keep him out of living room when we needed but it also meant he could still see us so he didn't feel too left out etc.
When we brought DD home, we made sure we made a huge fuss of the dog. I had been in hospital for 3 days and by his reaction when he saw me, he knew something had happened. We then took DD into living room and out her down into moses basket (Dog was left behind pet gate while we did this, so he could still see us while we put her down and settled her). After 10 mins or so we let the dog in to see what he did (DP stayed by his side at all times just in case he got a bit too excited!). But we shouldn't have been worried at all - his reaction was lovely. He put his nose on the side of the basket just to smell her, and then after a few seconds he just lay down next to the basket as if he were protecting her!
7 weeks on he is still amazing with her. He sits with us in the living room and naps at the same time as her. When he has to go in the kitchen and the pet gate is closed, he understands that that is where he has to be for a while. There are times he cries, but that is only because he wants to sit with us!
Even though the dog is great with DD, I would NEVER leave them on their own in a room together - you never know what can happen. Saying this, I know when DD is older, they are going to be inseparable! He adores her and is so protective of her.
IMO, the worst thing you can do is NOT introduce dog to DC, he will resent DC if its only ever been you and your pet.