Some departments are really cool about bringing children to the office. Other departments are really uptight about the noise that an infant or toddler might make. The same analysis applies to dogs, plus some arguments about sanitation/allergies. I think it is important to gauge the norm before bringing either over.
I've brought both to the various places I've worked, including yesterday, to a department where I've seen more dogs than kids around.
I brought Epsilon by the office after daycare because I'd forgotten to grab a few things. While I'm getting things together, the guy a few doors down walks down the hall with his dog and a graduate student he seems to want to talk to (or maybe its the grad student who wants to talk to him?) The owner and parent introduce the dog and the child to each other, and watch them play, while the graduate student awkwardly stands by. The owner goes into his office, the dog and Epsilon follow. When I go to retrieve Epsilon, the owner welcomes him in. The graduate student awkwardly tries to talk to Epsilon. The owner apologizes to the graduate student and plays with Epsilon and the dog. Eventually I decide that risking upsetting Epsilon's by the lack of a dog is better than taking up more of the graduate student's time, and take my (predictably screaming) toddler away. If I knew who the graduate student was, I'd write him an apology.
This entire interaction made me feel intensely awkward. Maybe it is because I am very sensitive to Epsilon screaming in public spaces, especially work spaces. Maybe because I didn't know how to respond to being an intruder in someone else's professional interaction (where I don't know either party particularly well). Maybe it's because people act very strangely around dogs and children.