We're in a similar position, I have a toddler, due second baby in October, and we now have an 8 week old puppy who just came home with us this week. It is like having a new baby already, he is quite well behaved so far really, but he cries from quite early in the morning for various reasons, thought I had a while yet before being woken up at silly hours again! It wasn't planned this way, it was my DH who has always wanted a dog and been nagging me for the last 7 years, and I only finally agreed as we went through three losses and I was convinced we wouldn't be able to have any more babies, and felt guilty that it was me stopping him having a dog and then another baby, so I gave in over the dog, and now I'm over 17 weeks pregnant.
I'm constantly being told I must be crazy and will have my hands full etc, but I'm hoping the puppy will be well on the way to being trained and well settled in by the time the new baby arrives, and at least I'll be home a lot to be able to look after him properly rather than being at work a lot. We thought it would be good for our toddler to have a furry friend but she seems very jealous of him, so it's like a little taste of what life may be like with her when the new baby arrives too!