The Home Care/Child Care program is only available to those working in Canada right now, based on small quotas and opens once a year for a day. If you are in Quebec you can look into a LMIA since you have posted the job on Job Bank and job sites and have proven you cannot find any Canadian who has the skills and education to do the job. You will have documented the recruitment process to show that no Canadian/PR has the education, language skills and work experience to do the job, only the caregiver you want to hire has the experience.
Make sure your caregiver gets ECA done for education that matches NOC, job letters with bank statements/pay stubs, and takes language tests including French.