"call Doctor" is a very old-fashioned way of saying "I'll call Dr ___". It's a replacement for the name, but I can't imagine people using it these days, unless they were perhaps a nurse talking to a frightened child.

"baby" is used when the baby doesn't have a name yet, or it can be used in place of the name if you want to be cute-sy!

Normal usage in the UK of wife would be "my wife" unless the man is very old, or young but being sexist or 'ironically sexist', making a joke like "oh, I've left the wife in the kitchen". If you could reasonably substitute wife for a term like "ball and chain" in the sentence then "the wife" would be correct, otherwise you're best using "my wife".

Yay language :D