Bearing in mind your child is just about to start being mobile, then no, do you really want a crawling, cruising, walking toddler whilst house training/generally training a pup? Completely bonkers
Have you seen the multiple threads that get posted with predictable regularity about how hard and horrible pups are, how people 'do loads of research' and still hate their pups and want to give them back? Sometimes after days or weeks, never mind months? 'He's jumping up/chewing/nipping' etc - ie normal puppy behaviour
I've always had dogs, and have had 3 pups in the last 6 years, and every time I forget how much hard work they are, the initial toilet training, settling them at night, needle sharp teeth and claws that constantly scrape at you, then they get to 5-8 months, no longer little and cute, and become wilful and obstinate and stop doing what you've just trained them to do, pulling on the lead, ignoring recall - my youngest dog is just turned 2 and finally fairly sensible and predictable, most of the time 
Leave it a couple of years, until your child is older, can understand instructions to leave the pup alone when necessary, and when you'll have more time to devote to training (pups can require intensive, repetitive training for up to 18 months depending on personality/breed) and save yourself, your child, and the pup from a whole lot of stress