Once you are in Canada as a PR, you can get any job you wish to without any restrictions, and that includes a babysitting job. You cannot, however, use an offer for a babysitting job in Canada for FSWP/FSTP/CEC, since those programs stipulate certain NOC categories, which babysitting/caregiver would not fall under.
To answe your question- you are free to do this job when you get to Canada as a PR, and you can (and should) even tell IRCC about it now. Just don't expect it to help you with the application process much, not until you switch to a specific immigration stream for caregivers/babysitters.
