I dont see a requirement for the child needs to be inside Canada while sending the application.
Give mailing address in canada so that you can receive communication if any, even though nowadays its all in email(except for final certificate of course).
So just send the application with current home address and give it a shot. Nothing to loose as you are not lying about anything hence you can see if you need to really travel to make an application(i doubt that would be necessary).
Also for sure, they will ask at the end to know when the child will travel to canada for oath as i have seen posts for the same as we cannot take oath outside.
No idea about processing time but for adults it varies from 1-2 years, depends on officer, officer, files complexity etc.
Follow instructions and submit necessary documents rather asking over here as rules change all the time.
https://www.canada.ca/en/immigration-refugees-citizenship/services/application/application-forms-guides/application-canadian-citizenship-minors.html
As armoured said, i assume you are citizen by naturalization hence you are now applying for your child.