As a PR, you have to be living in Canada to sponsor. If you were a citizen, you could sponsor from outside Canada. It doesn't matter how old the child is. I am sure they do not sort childrens PR applications by age.
You said that you only have a few months yourself before you lose your PR status due to residency requirements. Aside from the sponsorship problem, you will soon have to go to Canada yourself and stay for 2 years to keep your own PR. You can not sponsor your child if you lose your PR.