I wouldn't do it.... but that is because we have a big fat black lab, 3 cats, 4 kids (one under 18m) and NO time left for anything else!!
You would have to look at the usual questions. Do you have time and patience to train a puppy? May not be a good idea to have him/her thrust into a group of rambunctious kids, so where can the pup go for some quiet if he/she needs? Are you ok with cleaning up the inevitable messes and chewed up things?
In theory, I would love to get a new puppy. I have already thought about what breed, and everything, LoL. But I just know that it would be a bad idea, RIGHT NOW. So you just have to decide for your family!
Good luck!!