Congratulations Abhinav, firstly hoping that both the mother and the child are doing well. We were in the same boat last year, my wife was pregnant (I wasn’t 
) at the time of landing, we wanted our child to be a US Citizen so we made the final move after his birth when he turned 6 months and we felt comfortable traveling with him.
You can’t get your child a PR before you move to Canada. This is because only Canadian Citizens can sponsor individuals when the sponsor is outside Canada and that too if they commit to stay with the sponsored individual in Canada post approval. Permanent residents need to be in Canada when sponsoring dependents.
My child’s application hasn’t been completed yet, the current status is that the Application for Sponsorship has been approved and the PR application is in process; the medical tests have been done and received. It’s been 8 months since I first filed the application. I didn’t consult any immigration attorney or consultant but simply followed the instructions in the application package online to fill in and submit the application.
In my province (BC), applicants who have pending PR applications are eligible for Provincial Health Insurance(MSP). During the waiting period, first we had our US health insurance active and then Provincial Replacement Coverage through our employer till MSP kicked in.
Hope this helps.