f you’re the spouse, common-law partner or a family member of someone studying temporarily in Canada, you need a work permit to work in Canada.If you’re the spouse, common-law partner or a family member of someone working temporarily in Canada, you need a work permit to work in Canada.
You may be eligible for an open work permit if you’re
the spouse or common-law partner of a skilled worker in an occupation under the National Occupational Classification (NOC) skill type 0 or skill levels A or B
The skilled worker must be authorized to work for at least 6 months after you apply for your work permit.
the spouse or common-law partner of someone accepted for the Atlantic Immigration Program in a job under NOC skill type 0 or skill levels A, B or C
the spouse or common-law partner of a Quebec Selection Certificate (CSQ) holder who is eligible for the International Mobility Program Plus
a family member of a foreign representative
a family member of a foreign military member who is working in Canada
From the list of eligible persons/conditions for open work permit, there is no where mentioned this about dependent children
You may be eligible for an open work permit if you’re the spouse or common-law partner of a foreign student at a public post-secondary school, such as a college or university, or a collège d’enseignement général et professionnel (CEGEP) in Quebec. To be eligible, the student must be in a post-graduation work permit-eligible program of study.
Your work permit won’t be valid longer than your spouse’s or common-law partner’s study permit.
You also need to meet the general eligibility requirements for a work permit.
But it is mentioned here, a dependent child is a family member